The Cycle-Complete Graph Ramsey Numbers R(Cn, K8), For 10 ≤ n ≤ 15

Abstract

Given two graphs H1 and H2, the Ramsey number R(H1,H2) is the smallest natural number n such that each graph of order n contains a copy of H1 or its complement contains a copy of H2. In this paper, we find the exact Ramsey number R(Cn,K8) for 10 ≤ n ≤ 15, where Cn is the cycle on n vertices and K8 is the complete graph of order 8.

Key words and phrases. Ramsey number, cycle graph, complete graph.

2010 Mathematics Subject Classification. 05C55