On the Ramsey Number for Theta Graphs Versus the Complete Graph of Order Six

Abstract

The Ramsey number rG,H is the smallest positive integer n such that any graph W of order n contains G as a subgraph or its complement contains H as a subgraph. In this paper, we find the exact value for the Ramsey number rθn,K6;k≥6; n≥6, where θn is a theta graph of order n and K6 is the complete graph of order 6.