The Ramsey Numbers for Theta Graphs Versus the Wheel of Order (October 2016)
The Department of Mathematics and Statistics of the AUS College of Arts and Sciences cordially invites you to a seminar to be conducted by Dr. Mohammad Bataineh from Mathematics Department of
Abstract
The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F, the Ramsey number R(S,F) is the smallest positive integer r such that for every graph G on r vertices, G contains a graph in S as a subgraph or the complement of G contains F as a subgraph. Ramsey numbers of various graphs including theta graphs and wheels have been extensively studied. We extend known results in the area by presenting exact values of the Ramsey numbers R(θ_{n},W₅) for n≥5, where θ_{n} is the set of theta graphs of order n and W₅ is the wheel graph of order 5.
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