A note on the Ramsey numbers for theta graphs versus the wheel of order 5

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(?n,W5) for n?7, where ?n is the set of theta graphs of order n and W5 is the wheel graph of order 5. ? 2017