 PHD CONFIRMATION SEMINAR
 Speaker: Sogol Mohammadian, The University of Newcastle
 Title: Hamiltonian cycle problem and Markov chains
 Location: Room V107, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 10:00 am, Fri, 12^{th} May 2017
 Abstract:
In this talk we discuss a new approach for the Hamilton cycle problem (HCP). The HCP is one of the classical problems in combinatorial mathematics. It can be stated as given a graph G, find a cycle that passes through every single vertex exactly once, or determine that such a cycle does not exist. In 1994, Filar and Krass developed a new model for HCP by embedding this problem into a Markov decision process. This approach was the motivation of a new line research which was extended by several other people afterwards. In this approach, a new polytope corresponding to a given graph G was constructed and searching for Hamiltonian cycles in a given Hamiltonian graph G was converted to searching for particular extreme points (called Hamiltonian extreme points) among extreme points of that polytope. In this research, we are going to design a Markov chain with certain properties to sample Hamiltonian extreme points of that polytope. More precisely, we would like to study a specific class of input graphs, the socalled random graphs. Some preliminary theoretical results are presented in this talk.
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