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

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 and a graph , the Ramsey number is the smallest positive integer such that for every graph on vertices, contains a graph in as a subgraph or the complement of contains 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 for , where is the set of theta graphs of order and is the wheel graph of order .

Keywords

• ramsey number
• theta graph
• wheel
• extremal graph theory