On the cycle-path bipartite Ramsey number

Abstract

For bipartite graphs G1,G2,…,Gk, the bipartite Ramsey number b(G1,G2, …,Gk) is the least positive integer b, so that any coloring of the edges of Kb,b with k colors, will result in a copy of Gi in the ith color, for some i. In this paper we will show that if s is an integer such that s≥max⁡{18,(b(C34,C34)+1)/2}, then b(C2s,P2s)=2s−1.