On k-Ramsey Numbers of Stripes

Abstract

For bipartite graphs F and H with Ramsey number R(F, H) = n and an integer k with 2 < k < n, the k-Ramsey number of F and H is the minimum order of a balanced complete k-partite graph G for which every red-blue coloring of G results in a subgraph of G isomorphic to F all of whose edges are colored red or a subgraph isomorphic to H all of whose edges are colored blue. In this work, we investigate the k-Ramsey numbers Rk(F}H) for certain stripes F and H (1-regular graphs) and for certain values of k. We also include a discussion of A:-Ramsey numbers of graphs that are not bipartite. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.