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### CARMA-Sponsored Seminar Series: Colloquia, Seminars and More.

[Note: events are listed by descending date.]
 CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Sudeep Stephen, The University of Newcastle Title: The Forcing Number of Graphs with Given Girth Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Mon, 14th Nov 2016 Abstract: For a two-coloring of the vertex set of a simple graph $G$ consider the following color-change rule: a red vertex is converted to blue if it is the only red neighbor of some blue vertex. A vertex set $S$ is called zero-forcing if, starting with the vertices in $S$ blue and the vertices in the complement $V \setminus S$ red, all the vertices can be converted to blue by repeatedly applying the color-change rule. The minimum cardinality of a zero-forcing set for the graph $G$ is called the zero-forcing number of $G$, denoted by $Z(G)$. There is a conjecture connecting zero forcing number, minimum degree $d$ and girth $g$ as follows: "If G is a graph with girth $g \geq 3$ and minimum degree $d \geq 2$, then $Z(G) \geq d+ (d-2)(g-3)$". I shall discuss a recent paper where the conjecture is proved to be true for all graphs with girth \leq 10. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Hoffman-Singleton paper of 1964 Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Mon, 7th Nov 2016 Abstract: Today's discrete mathematics seminar is dedicated to Mirka Miller. I am going to present the beautiful Hoffman-Singleton (1964) paper which established the possible values for valencies for Moore graphs of diameter 2, gave us the Hoffman-Singleton graph of order 50, and gave us one of the intriguing still unsettled problems in combinatorics. The proof is completely linear algebra and is a proof that any serious student in discrete mathematics should see sometime. This is the general area in which Mirka made many contributions. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Essential Points Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Mon, 31st Oct 2016 Abstract: This afternoon (31 October) we shall complete the discussion about vertex-minimal graphs with dihedral automorphism groups. I have attached an outline of what was covered in the first two weeks. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Minimal-order graphs with dihedral automorphism group Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Mon, 24th Oct 2016 Abstract: This week we shall continue by introducing the cast of characters to be used for producing minimal-order graphs with dihedral automorphism group. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Graphs And Their Automorphism Groups Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Mon, 17th Oct 2016 Abstract: Konig (1936) asked whether every finite group G is realized as the automorphism group of a graph. Frucht answered the question in the affirmative and his answer involved graphs whose orders were substantially bigger than the orders of the groups leading to the question of finding the smallest graph with a fixed automorphism group. We shall discuss some of the early work on this problem and some recent results for the family of dihedral groups. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Judy-anne Osborn, CARMA, The University of Newcastle Title: A visual combinatorial interpretation of the Kolakoski density question Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 8th Jun 2016 Abstract: The density of 1's in the Kolakoski sequence is conjectured to be 1/2. Proving this is an open problem in number theory. I shall cast the density question as a problem in combinatorics, and give some visualisations which may suggest ways to gain further insight into the conjecture. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: Suk's proof of the asymptotic Erdos-Szekeres conjecture Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 1st Jun 2016 Abstract: I continue the discussion of the Erdos-Szekeres conjecture about points in convex position with an outline of the recent proof of an asymptotic version of the conjecture. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: The Erdos-Szekeres conjecture about points in convex position Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 25th May 2016 Abstract: In 1935 Erdos and Szekeres proved that there exists a function f such that among f(n) points in the plane in general position there are always n that form the vertices of a convex n-gon. More precisiely, they could prove a lower and an upper bound for f(n) and conjectured that the lower bound is sharp. After 70 years with very limited progress, there have been a couple of small improvements of the upper bound in recent years, and finally last month Andrew Suk announced a huge step forward: a proof of an asymptotic version of the conjecture. I plan two talks on this topic: (1) a brief introduction to Ramsey theory, and (2) an outline of Suk's proof. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Sudeep Stephen, School of Mathematical and Physical Sciences, The University of Newcastle Title: Zero Forcing Number of a Graph Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 18th May 2016 Abstract: Zero forcing number, Z(G), of a graph G is the minimum cardinality of a set S of black vertices (whereas vertices in V (G)\S are colored white) such that V (G) is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. Zero forcing number was introduced by the "AIM Minimum Rank – Special Graphs Work Group". In this talk, I present an overview of the results obtained from their paper. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Cyriac Grigorious, The University of Newcastle Title: Dimensions of Cayley (Di)graphs Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 27th Apr 2016 Abstract: A metric generator is a set W of vertices of a graph G such that for every pair of vertices u,v of G, there exists a vertex w in W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. In this case the vertex w is said to resolve or distinguish the vertices u and v. The minimum cardinality of a metric generator for G is called the metric dimension. The metric dimension problem is to find a minimum metric generator in a graph G. In this talk I am discussing about the metric dimension and partition dimension of Cayley (di)graphs. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Sequenceable and R-sequenceable groups Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 13th Apr 2016 Abstract: This week I shall finish my discussion of sequenceable and R-sequenceable groups. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Circulant graphs isomorphic to Cartesian products of cycles Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Sun, 10th Apr 2016 Abstract: I am now refereeing a manuscript on the above and I’ll tell you about its contents. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Orthogonalizeable groups Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 6th Apr 2016 Abstract: B. Gordon (1961) defined sequenceable groups and G. Ringel (1974) defined R-sequenceable groups. Friedlander, Gordon and Miller conjectured that finite abelian groups are either sequenceable or R-sequenceable. The preceding definitions are special cases of what T. Kalinowski and I are calling an orthogonalizeable group, namely, a group for which every Cayley digraph on the group admits either an orthogonal directed path or an orthogonal directed cycle. I shall go over the history and current status of this topic along with a discussion about the completion of a proof of the FGM conjecture. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: Discrepancy in graphs Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 30th Mar 2016 Abstract: The discrepancy of a graph measures how evenly its edges are distributed. I will talk about a lower bound which was proved by Bollobas and Scott in 2006, and extends older results by Erdos, Goldberg, Pach and Spencer. The proof provides a nice illustration of the probabilistic method in combinatorics. If time allows I will outline how this stuff can be used to prove something about convex hulls of bilinear functions. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: A/Prof. Michael Coons, CARMA, The University of Newcastle Title: Minimal growth of some structured $\pm 1$-sequences Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 16th Mar 2016 Abstract: In this talk, I will outline my interest in, and results towards, the Erdős Discrepancy Problem (EDP). I came about this problem as a PhD student sometime around 2007. At the time, many of the best number theorists in the world thought that this problem would outlast the Riemann hypothesis. I had run into some interesting examples of some structured sequences with very small growth, and in some of my early talks, I outlined a way one might be able to attack the EDP. As it turns out, the solution reflected quite a bit of what I had guessed. And I say 'guessed' because I was so young and naïve that my guess was nowhere near informed enough to actually have the experience behind it to call it a conjecture. In this talk, I will go into what I was thinking and provide proof sketches of what turn out to be the extremal examples of EDP. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: The union-closed sets conjecture Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 9th Mar 2016 Abstract: I'll continue to discuss Frankl's union-closed sets conjecture. In particular I'll present two possible approaches (local configurations and averaging) and indicate obstacles to proving the general case using these methods. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: The union-closed sets conjecture Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 2nd Mar 2016 Abstract: Peter Frankl's union-closed sets conjecture, which dates back to (at least) 1979, states that for every finite family of sets which is closed under taking unions there is an element contained in at least half of the sets. Despite considerable efforts the general conjecture is still open, and the latest polymath project is an attempt to make progress. I will give an overview of equivalent variants of the conjecture and discuss known special cases and partial results. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dominique Buset, unknown or leave blank, Title: The Degree/Diameter Problem for Mixed Graphs Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 11:00 am, Thu, 11th Feb 2016 Abstract: The Degree/Diameter Problem for graphs has its motivation in the efficient design of interconnection networks. It seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity is focussed on finding new examples of graphs or families of graph with orders approaching the bound as closely as possible. This problem was first mention in 1964 and has its motivation in the efficient design of interconnection networks. A lot of great mathematician studied this problem and obtained some results but there still remain a lot of unsolved problems about this subject. Our regretted professor Mirka Miller has given a great expansion to this problems and a lot of new results were given by her and her students. One of the problem she was recently interested in, was the Degree/Diameter problem for mixed graphs i.e. graphs in which we allow undirected edges and arcs (directed edges). Some new result about the upper bound of this Moore mixed graph has been obtained in 2015. So this talk consists on giving the main known results about those graphs. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Paul Leopardi, unknown or leave blank, Title: Finding quadrature points in a sparse grid: a down-set constrained binary knapsack problem Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 22nd Oct 2015 Abstract: A dimension adaptive algorithm for sparse grid quadrature in reproducing kernel Hilbert spaces on products of spheres uses a greedy algorithm to approximately solve a down-set constrained binary knapsack problem. The talk will describe the quadrature problem, the knapsack problem and the algorithm, and will include some numerical examples. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: The Kemnitz conjecture and other zero-sum problems Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 10th Sep 2015 Abstract: I will complete the proof of the Kemnitz conjecture and make some remarks about related zero-sum problems. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: Using polynomials to prove things in combinatorics Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 3rd Sep 2015 Abstract: After briefly describing a few more simple applications of Alon's Nullstellensatz, I will present in detail Reiher's amazing proof of the Kemnitz conjecture regarding lattice points in the plane. Download: Seminar slides (148K) [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: Combinatorial Nullstellensatz Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 27th Aug 2015 Abstract: Noga Alon's Combinatorial Nullstellensatz, published in 1999, is a statement about polynomials in many variables and what happens if one of these vanishes over the set of common zeros of some others. In contrast to Hilbert's Nullstellensatz, it makes strong assumptions about the polynomials it is talking about, and this leads a tool for producing short and elegant proofs for numerous old and new results in combinatorial number theory and graph theory. I will present the proof of the algebraic result and some of the combinatorial applications in the 1999 paper. Download: Seminar slides (208K) [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Yuqing Lin, School of Electrical Engineering and Computer Science, The University of Newcastle Title: Edge disjoint perfect matchings in regular graph Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 13th Aug 2015 Abstract: Existing of perfect matchings in regular graph is a fundamental problem in graph theory, and it closely model many real world problems such as broadcasting and network management. Recently, we have studied the number of edge disjoint perfect matching in regular graph, and using some well-known results on the existence of perfect matching and operations forcing unique perfect matchings in regular graph, we are able to make some pleasant progress. In this talk, we will present the new results and briefly discuss the proof. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Paul Samuel, Kuwait University Title: Convex Partition and Graph Embedding Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 6th Aug 2015 Abstract: Partitioning is a basic fundamental technique in graph theory. Graph partitioning technique is used widely to solve several combinatorial problems. We will discuss the role of edge partitioning techniques on graph embedding. The graph embedding includes some combinatorial problems such as bandwidth problem, wirelength problem, forwarding index problem etc and in addition includes some cheminformatics problems such as Wiener Index, Szeged Index, PI index etc. In this seminar, we study convex partition and its characterization. In addition, we also analyze the relationship between convex partition and some other edge partitions such as Szeged edge partition and channel edge partition. The graphs that induce convex partitions are bipartite. We will discuss the difficulties in extending this technique to non-bipartite graphs. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Several Beautiful Proofs Location: Room V31, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Wed, 29th Jul 2015 Abstract: Mathematicians sometimes speak of the beauty of mathematics which to us is reflected in proofs and solutions for the most part. I am going to give a few proofs that I find very nice. This is stuff that post-grad discrete students certainly should know exists. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Padraig Ó Catháin , unknown or leave blank, Title: Unbiased bases, uncertainty principles and trades in Hadamard matrices Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Wed, 27th May 2015 Abstract: Arising originally from the analysis of a family of compressed sensing matrices, Ian Wanless and I recently investigated a number of linear algebra problems involving complex Hadamard matrices. I will discuss our main result, which relates rank-one submatrices of Hadamard matrices to the number of non-zero terms in a representation of a fixed vector with respect to two unbiased bases of a finite dimensional vector space. Only a basic knowledge of linear algebra will be assumed. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Paul Leopardi, unknown or leave blank, Title: Twin bent functions, Cayley graphs, and Radon-Hurwitz theory Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Wed, 29th Apr 2015 Abstract: I have recently [2] shown that each group $Z_2^{2m}$ gives rise to a pair of bent functions with disjoint support, whose Cayley graphs are a disjoint pair of strongly regular graphs $\Delta_m[-1]$, $\Delta_m[1]$ on $4^m$ vertices. The two strongly regular graphs are twins in the sense that they have the same parameters $(\nu, k, \lambda, \mu)$. For $m < 4$, the two strongly regular graphs are isomorphic. For $m \geq 4$, they are not isomorphic, because the size of the largest clique differs. In particular, the largest clique size of $\Delta_m[-1]$ is $\rho(2^m)$ and the largest clique in $\Delta_m[1]$ has size at least $2^m$, where $\rho(n)$ is the Hurwitz-Radon function. This non-isomorphism result disproves a number of conjectures that I made in a paper on constructions of Hadamard matrices [1]. [1] Paul Leopardi, "Constructions for Hadamard matrices, Clifford algebras, and their relation to amicability - anti-amicability graphs", Australasian Journal of Combinatorics, Volume 58(2) (2014), pp. 214–248. [2] Paul Leopardi, "Twin bent functions and Clifford algebras", accepted 13 January 2015 by the Springer Proceedings in Mathematics and Statistics (PROMS): Algebraic Design Theory and Hadamard Matrices (ADTHM 2014). [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: Combinatorics of data recovery in distributed databases Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Wed, 1st Apr 2015 Abstract: I will discuss a combinatorial problem coming from database design. The problem can be interpreted as maximizing the number of edges in a certain hypergraph subject to a recoverability condition. It was solved recently by the high school student Max Aehle, who came up with a nice argument using the polynomial method. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Pancyclicty and Cayley graphs on generalized dihedral groups Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Wed, 25th Mar 2015 Abstract: This week I shall conclude my discussion of pancyclicity and Cayley graphs on generalized dihedral groups. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Pancyclicty and Cayley graphs on generalized dihedral groups Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Wed, 18th Mar 2015 Abstract: This is joint work with our former honours student Alex Muir. We look at the variety of lengths of cycles in Cayley graphs on generalized dihedral groups. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Pancyclicty and Cayley graphs on generalized dihedral groups Location: Room VG25, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Wed, 11th Mar 2015 Abstract: This is joint work with our former honours student Alex Muir. We look at the variety of lengths of cycles in Cayley graphs on generalized dihedral groups. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Yuqing Lin, School of Electrical Engineering and Computer Science, The University of Newcastle Title: The number of maximal state circles of plane graphs Location: Room V106, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 2:00 pm, Thu, 5th Mar 2015 Abstract: It is well known that there is a one-to-one correspondence between signed plane graphs and link diagrams via the medial construction. The relationship was once used in knot tabulations in the early time of study in knot theory. Indeed, it provides a method of studying links using graphs. Let $G$ be a plane graph. Let $D(G)$ be the alternating link diagram corresponding to the (positive) $G$ obtained from the medial construction. A state $S$ of $D$ is a labeling each crossing of $D$ by either $A$ or $B$. Making the corresponding split for each crossing gives a number of disjoint embedded closed circles, called state circles. We call a state which possesses maximum number of state circles a maximum state. The maximum state is closely related to the genus of the corresponding link, thus has been studied. In this talk, we will discuss some of the recent progress we have made on this topic. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Searching Graphs: IV Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 2nd Oct 2014 Abstract: This week I shall finish my discussion about searching graphs by looking at the recent paper by Clarke and MacGillavray that characterizes graphs that are k-searchable. [Permanent event link] CARMA COMBINATORICS SEMINAR Speaker: Dr Paul Leopardi, Australian National University Title: Twin bent functions and Clifford algebras Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 25th Sep 2014 Abstract: It is known that the function s defined on an ordering of the 4^m monomial basis matrices of the real representation of the Clifford algebra Cl(m, m), where s(A) = 0 if A is symmetric, s(A) = 1 if A is skew, is a bent function. It is perhaps less well known that the function t, where t(A) = 0 if A is diagonal or skew, t(A) = 1 otherwise, is also a bent function, with the same parameters as s. The talk will describe these functions and their relation to Hadamard difference sets and strongly regular graphs. The talk was originally presented at ADTHM 2014 in Lethbridge this year. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Graph searching characterization results Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 18th Sep 2014 Abstract: This Thursday, sees a return to graph searching in the discrete mathematics instructional seminar. I’ll be looking at characterization results. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Indra Rajasingh, School of Advanced Sciences, VIT University Title: Improved bound for Locating-Total Domination Number of Regular Graphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 28th Aug 2014 Abstract: A locating-total dominating set (LTDS) in a connected graph G is a total dominating set $S$ of $G$ such that for every two vertices $u$ and $v$ in $V(G)-S$, $N(u) \cap S \neq N(v) \cap S$. Determining the minimum cardinality of a locating-total dominating set is called as the locating-total dominating problem and it is denoted as $\gamma_t^l (G)$. We have improved the lower bound obtained by M.A.Henning and N.D.Rad [1]. We have also proved that the bound obtained is sharp for some special families of regular graphs. [1] M. A. Henning and N. J. Rad, Locating-total dominations in graphs, Discrete Applied Mathematics, 160(2012), 1986-1993. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Searching graphs embedded on the torus Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 21st Aug 2014 Abstract: Brian Alspach will continue discussing searching graphs embedded on the torus. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Basic Pursuit-Evasion In Graphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 14th Aug 2014 Abstract: This week I shall continue the discussion of searching graphs. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Basic Pursuit-Evasion In Graphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 7th Aug 2014 Abstract: This week I shall start a series of talks on basic pursuit-evasion in graphs (frequently called cops and robber in the literature). We shall do some topological graph theory leading to an intriguing conjecture, and we'll look at a characterization problem. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: A graph theory research project Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 31st Jul 2014 Abstract: I shall be describing a largely unexplored concept in graph theory which is, I believe, an ideal thesis topic. I shall be presenting this at the CIMPA workshop in Laos in December. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: A new graph construction using groups Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 10th Jul 2014 Abstract: We shall finish our look at two-sided group graphs. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: A new graph construction using groups Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 26th Jun 2014 Abstract: I am refereeing a manuscript in which a new construction for producing graphs from a group is given. There are some surprising aspects of this new method and that is what I shall discuss. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Mr Ben Brawn, School of Mathematical and Physical Sciences, The University of Newcastle Title: Quasi-regular trees Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 22nd May 2014 Abstract: The idea of an almost automorphisms of a tree will be introduced as well as what we are calling quasi-regular trees. I will then outline what I have been doing in regard to the almost automorphisms of almost quasi-regular trees with two valencies and the challenges that come with using more valencies. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: The Oberwolfach Problem Re-Visited Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 15th May 2014 Abstract: This year is the fiftieth anniversary of Ringel's posing of the well-known graph decomposition problem called the Oberwolfach problem. In this series of talks, I shall examine what has been accomplished so far, take a look at current work, and suggest a possible new avenue of approach. The material to be presented essentially will be self-contained. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: The Oberwolfach Problem Re-Visited Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 8th May 2014 Abstract: This year is the fiftieth anniversary of Ringel's posing of the well-known graph decomposition problem called the Oberwolfach problem. In this series of talks, I shall examine what has been accomplished so far, take a look at current work, and suggest a possible new avenue of approach. The material to be presented essentially will be self-contained. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: The Oberwolfach Problem Re-Visited Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 17th Apr 2014 Abstract: This year is the fiftieth anniversary of Ringel's posing of the well-known graph decomposition problem called the Oberwolfach problem. In this series of talks, I shall examine what has been accomplished so far, take a look at current work, and suggest a possible new avenue of approach. The material to be presented essentially will be self-contained. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: The proof of Manickam-Miklos-Singhi Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 10th Apr 2014 Abstract: : In this final talk of the sequence we will sketch Blinovsky's recent proof of the conjecture: Whenever n is at least 4k, and A is a set of n numbers with sum 0, then there are at least (n-1) choose (k-1) subsets of size k which have non-negative sum. The nice aspect of the proof is the combination of hypergraph concepts with convex geometry arguments and a Berry-Esseen inequality for approximating the hypergeometric distribution. The not so nice aspect (which will be omitted in the talk) is the amount of very tedious algebraic manipulation that is necessary to verify the required estimates. There are slides for all four MMS talks here. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: From EKR to MMS Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 3rd Apr 2014 Abstract: The Erdos-Ko-Rado (EKR) Theorem is a classical result in combinatorial set theory and is absolutely fundamental to the development of extremal set theory. It answers the following question: What is the maximum size of a family F of k-element subsets of the set {1,2,...,n} such that any two sets in F have nonempty intersection? In the 1980's Manickam, Miklos and Singhi (MMS) asked the following question: Given that a set A of n real numbers has sum zero, what is the smallest possible number of k-element subsets of A with nonnegative sum? They conjectured that the optimal solutions for this problem look precisely like the extremal families in the EKR theorem. This problem has been open for almost 30 years and many partial results have been proved. There was a burst of activity in 2012, culminating in a proof of the conjecture in October 2013. This series of talks will explore the basic EKR theorem and discuss some of the recent results on the MMS conjecture. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: From EKR to MMS Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 20th Mar 2014 Abstract: The Erdos-Ko-Rado (EKR) Theorem is a classical result in combinatorial set theory and is absolutely fundamental to the development of extremal set theory. It answers the following question: What is the maximum size of a family F of k-element subsets of the set {1,2,...,n} such that any two sets in F have nonempty intersection? In the 1980's Manickam, Miklos and Singhi (MMS) asked the following question: Given that a set A of n real numbers has sum zero, what is the smallest possible number of k-element subsets of A with nonnegative sum? They conjectured that the optimal solutions for this problem look precisely like the extremal families in the EKR theorem. This problem has been open for almost 30 years and many partial results have been proved. There was a burst of activity in 2012, culminating in a proof of the conjecture in October 2013. This series of talks will explore the basic EKR theorem and discuss some of the recent results on the MMS conjecture. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: From EKR to MMS Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 13th Mar 2014 Abstract: The Erdos-Ko-Rado (EKR) Theorem is a classical result in combinatorial set theory and is absolutely fundamental to the development of extremal set theory. It answers the following question: What is the maximum size of a family F of k-element subsets of the set {1,2,...,n} such that any two sets in F have nonempty intersection? In the 1980's Manickam, Miklos and Singhi (MMS) asked the following question: Given that a set A of n real numbers has sum zero, what is the smallest possible number of k-element subsets of A with nonnegative sum? They conjectured that the optimal solutions for this problem look precisely like the extremal families in the EKR theorem. This problem has been open for almost 30 years and many partial results have been proved. There was a burst of activity in 2012, culminating in a proof of the conjecture in October 2013. This series of talks will explore the basic EKR theorem and discuss some of the recent results on the MMS conjecture. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Ilaria Castellano, University of Bari Aldo Moro Title: The Rough Cayley Graph Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 7th Nov 2013 Abstract: The rough Cayley graph is the analogue in the context of topological groups of the standard Cayley graph, which is defined for finitely generated group. It will be shown how it is possible to associate such a graph to a compactly generated totally disconnected and locally compact (t.d.l.c.) group and how the rough Cayley graph represents an important tool to study the structure of this kind of group. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Rajan Bharati, Loyola College Title: Conditional Resolvability in Graphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 2:00 pm, Tue, 5th Nov 2013 Abstract: Let $G$ be a connected graph with vertex set $V$ and edge set $E$. The distance $d(u,v)$ between two vertices $u$ and $v$ in $G$ is the length of a shortest $u-v$ path in $G$. For an ordered set $W = \{w_1, w_2, ..., w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the code of $v$ with respect to $W$ is the $k$-vector $$C_W(v)=(d(v,w_1),d(v,w_2), ..., d(v,w_k)).$$ The set $W$ is a resolving set for $G$ if distinct vertices of $G$ have distinct codes with respect to $W$. A resolving set for $G$ containing a minimum number of vertices is called a minimum resolving set or a basis for $G$. The metric dimension, denoted, $dim(G)$ is the number of vertices in a basis for $G$. The problem of finding the metric dimension of an arbitrary graph is NP-complete. The problem of finding minimum metric dimension is NP-complete for general graphs. Manuel et al. have proved that this problem remains NP-complete for bipartite graphs. The minimum metric dimension problem has been studied for trees, multi-dimensional grids, Petersen graphs, torus networks, Benes and butterfly networks, honeycomb networks, X-trees and enhanced hypercubes. These concepts have been extended in various ways and studied for different subjects in graph theory, including such diverse aspects as the partition of the vertex set, decomposition, orientation, domination, and coloring in graphs. Many invariants arising from the study of resolving sets in graph theory offer subjects for applicable research. The theory of conditional resolvability has evolved by imposing conditions on the resolving set. This talk is to recall the concepts and mention the work done so far and future work. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Joe Ryan, School of Electrical Engineering and Computer Science, The University of Newcastle Title: Subgraph degree/diameter problem Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 10th Oct 2013 Abstract: TBA [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Edy Tri Baskoro, Institut Teknologi Bandung (ITB) Title: Necessary Conditions for the existence of Almost Moore Digraphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 26th Sep 2013 Abstract: It is well known that the Moore digraph, namely a diregular digraph of degree d, diameter k and order 1 + d + d 2 + ... + d k , only exists if d = 1 or k = 1. Let (d,k)-digraph be a diregular digraph of degree d ≥ 2, diameter k ≥ 2 and order d+d 2 +...+d k , one less than the Moore bound. Such a (d,k)-digraph is also called an almost Moore digraph. The study of the existence of an almost Moore digraph of degree d and diameter k has received much attention. Fiol, Allegre and Yebra (1983) showed the existence of (d,2)-digraphs for all d ≥ 2. In particular, for d = 2 and k = 2, Miller and Fris (1988) enumerated all non-isomophic (2,2)-digraphs. Furthermore, Gimbert (2001) showed that there is only one (d,2)-digraph for d ≥ 3. However for de- gree 2 and diameter k ≥ 3, it is known that there is no (2,k)-digraph (Miller and Fris, 1992). Furthermore, it was proved that there is no (3,k)-digraph with k ≥ 3 (Baskoro, Miller, Siran and Sutton, 2005). Recently, Conde, Gimbert, Gonzáles, Miret, and Moreno (2008 & 2013) showed that no (d,k)-digraphs exist for k = 3,4 and for any d ≥ 2. Thus, the remaining case still open is the existence of (d,k)- digraphs with d ≥ 4 and k ≥ 5. Several necessary conditions for the existence of (d,k)-digraphs, for d ≥ 4 and k ≥ 5, have been obtained. In this talk, we shall discuss some necessary conditions for these (d,k)-digraphs. Open problems related to this study are also presented. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Mirka Miller, School of Mathematical and Physical Sciences, The University of Newcastle Title: Constructions of large graphs and digraphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 19th Sep 2013 Abstract: TBA [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Mirka Miller, School of Mathematical and Physical Sciences, The University of Newcastle Title: Degree/Diameter Problem Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 12th Sep 2013 Abstract: The degree/diameter problem is to find the largest possible order of a graph (or digraph) with given maximum degree (or maximum out-degree) and given diameter. This is one of the unsolved problems in Extremal Graph Theory. Since the general problem is difficult many variations of the problem have been considered, including bipartite, vertex-transitive, mixed, planar, etc. This talk is part of a series started in May. The provisional schedule is 10 May Novi Bong: Proof of the non-existence of undirected Moore graphs for diameter 2 and 3 (Hoffman and Singleton, 1960) 5 September Guillermo Pineda-Villavicencio: New results in the degree/diameter problem for surfaces 12 September Mirka Miller: Repeats and mixed Moore graphs 19 September Mirka Miller: Constructions of large graphs and digraphs 26 September Edy Tri Baskoro: Repeat permutations in almost Moore digraphs Mid-semester break 10 October Joe Ryan: Subgraph degree/diameter problem Another break...to be continued in November [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Guillermo Pineda-Villavicencio, Collaborative Research Network, The University of Ballarat Title: On the maximum order of graphs embedded in surfaces Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 5th Sep 2013 Abstract: Joint work with David Wood (Monash University, Australia) and Eran Nevo (Ben-Gurion University of the Negev, Israel). The maximum number of vertices of a graph of maximum degree $\Delta\ge 3$ and diameter $k\ge 2$ is upper bounded by $\Delta^{k}$. If we restrict our graphs to certain classes, better upper bounds are known. For instance, for the class of trees there is an upper bound of $2\Delta^{\lfloor k/2\rfloor}$. The main result of this paper is that, for large $\Delta$, graphs embedded in surfaces of bounded Euler genus $g$ behave like trees. Specifically, we show that, for large $\Delta$, such graphs have orders bounded from above by \begin{cases} (c_0g+c_1)\Delta^{\lfloor k/2\rfloor} & \text{if $k$ is even}\\ (c_0g^2+c_1)\Delta^{\lfloor k/2\rfloor} & \text{if $k$ is odd} \end{cases} where $c_0,c_1$ are absolute constants. With respect to lower bounds, we construct graphs of Euler genus $g$, odd diameter and orders $(c_0\sqrt{g}+c_1)\Delta^{\lfloor k/2\rfloor}$, for absolute constants $c_0,c_1$. Our results answer in the negative a conjecture by Miller and Širáň (2005). Before this paper, there were constructions of graphs of Euler genus $g$ and orders $c_0\Delta^{\lfloor k/2\rfloor}$ for an absolute constant $c_0$. Also, Šiagiová and Simanjuntak (2004) provided an upper bound of $(c_0g+c_1)k\Delta^{\lfloor k/2\rfloor}$ with absolute constants $c_0,c_1$. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: Dependent Random Choice II Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 17th Nov 2011 Abstract: We look at (parts of) the survey paper Dependent Random Choice by Jacob Fox and Benny Sudakov: http://arxiv.org/abs/0909.3271. The abstract of the paper says "We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this survey we discuss some of them." My plan for the seminar is to start with a quick recap of the classics of extremal (hyper)graph theory (i.e. Turan, Ramsey, Ramsey-Turan), then look at some simple examples for the probabilistic method in action, and finally come to the striking applications mentioned in the quoted abstract. Only elementary probability is required. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: Review of "Dependent Random Choice" Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 10th Nov 2011 Abstract: We look at (parts of) the survey paper Dependent Random Choice by Jacob Fox and Benny Sudakov: http://arxiv.org/abs/0909.3271 The abstract of the paper says "We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this survey we discuss some of them." My plan for the seminar is to start with a quick recap of the classics of extremal (hyper)graph theory (i.e. Turan, Ramsey, Ramsey-Turan), then look at some simple examples for the probabilistic method in action, and finally come to the striking applications mentioned in the quoted abstract. Only elementary probability is required. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: More Cayley Digraphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 3rd Nov 2011 Abstract: This week we shall conclude our look at the paper by Dave Witte on Hamilton directed cycles in Cayley digraphs of prime power order. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Cayley Digraphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 27th Oct 2011 Abstract: We shall start looking at Dave Witte's (now Dave Morris) proof that connected Cayley digraphs of prime power order have Hamilton directed cycles. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Lovasz Problem Pt II Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 15th Sep 2011 Abstract: This week the discrete mathematics instructional seminar will continue with a consideration of the Lovasz problem. This is the last meeting of the seminar until 13 October. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Lovasz's Conjecture Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 8th Sep 2011 Abstract: The topic is Lovasz's Conjecture that all connected vertex-transitive graphs have Hamilton paths. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 1st Sep 2011 Abstract: This Thursday is your chance to start anew! I shall be starting a presentation of the best work that has been done on Lovasz's famous 1979 problem (now a conjecture) stating that every connected vertex-transitive graph has a Hamilton path. This is good stuff and requires minimal background. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: The 1960 Hoffman-Singleton Paper: Part III Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 25th Aug 2011 Abstract: This week we shall conclude the proof of the uniqueness of the Hoffman-Singleton graph. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: The 1960 Hoffman-Singleton Paper: Part III Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 18th Aug 2011 Abstract: We continue looking at the 1960 Hoffman-Singleton paper about Moore graphs and related topics. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS SEMINAR Speaker: Dr Uwe Leck, Department of Mathematics and Computer Science, University of Wisconsin-Superior Title: Orthogonal Double Covers of Graphs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Tue, 28th Jun 2011 Abstract: The concept of orthogonal double covers (ODC) of graphs originates in questions concerning database constraints and problems in statistical combinatorics and in design theory. An ODC of the complete graph $K_n$ by a graph $G$ is a collection of $n$ subgraphs of $K_n$, all isomorphic to $G$, such that any two of them share exactly one edge, and every edge of $K_n$ occurs in exactly two of the subgraphs. We survey some of the main results and conjectures in the area as well as constructions, generalizations and modifications of ODC. [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS SEMINAR Speaker: Ian Roberts, Charles Darwin University Title: The interplay of Extremal set theory and combinatorial designs Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:30 pm, Tue, 28th Jun 2011 Abstract: The talk will focus on recent results or work in progress, with some open problems which span both Combinatorial Design and Sperner Theory. The work focuses upon the duality between antichains and completely separating systems. An antichain is a collection $\cal A$ of subsets of $[n]=\{1,...,n\}$ such that for any distinct $A,B\in\cal A$, $A$ is not a subset of $B$. A $k$-regular antichain on $[m]$ is an antichain in which each element of $[m]$ occurs exactly $k$ times. A CSS is the dual of an antichain. An $(n,k)CSS \cal C$ is a collection of blocks of size $k$ on $[n]$, such that for each distinct $a,b\in [n]$ there are sets $A,B \in \cal C$ with $a \in A-B$ and $b \in B-A$. The notions of $k$-regular antichains of size $n$ on $[m]$ and $(n,k)CSS$s in $m$ blocks are dual concepts. Natural questions to be considered include: Does a $k$-regular antichain of size $n$ exist on $[m]$? For \$k [Permanent event link] CARMA-GTA DISCRETE MATHEMATICS INSTRUCTIONAL SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: The Edmonds-Fulkerson matroid partition theorem Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 5th May 2011 Abstract: We meet this Thursday at the usual time when I will show you a nice application of the Edmonds-Fulkerson matroid partition theorem, namely, I'll prove that Paley graphs have Hamilton decompositions (an unpublished result). [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Discrete Mathematics Instructional Seminar Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 14th Apr 2011 Abstract: This week we shall start the classical paper by Jack Edmonds and DR Fulkerson on partitioning matroids. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Discrete Maths Seminar Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 7th Apr 2011 Abstract: We shall conclude the discussion of some of the mathematics surrounding Birkhoff's Theorem about doubly stochastic matrices. [Permanent event link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Prof Brian Alspach, CARMA, The University of Newcastle Title: Discrete Maths Seminar: Introductions Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 24th Feb 2011 Abstract: This is a discrete mathematics instructional seminar commencing 24 February--to meet on subsequent Thursdays from 3:00-4:00 p.m. The seminar will focus on "classical" papers and portions of books. [Permanent event link]