The Set Multipartite Ramsey Numbers M_j(P_n, mK_2)

Abstract

For given two any graph H and G, the set multipartite Ramsey number M_j(G, H) is the smallest integer t such that for every factorization of graph K_(t×j):= F1 F2 so that F1 contains G as a subgraph or F2 contains H as a subgraph. In this paper, we determine M_j(P_n, mK_2) with j=3,4,5 and m>=2 where P_n denotes a path for n=2,3 vertices and mK_2 denotes a matching (stripes) of size m and pairwise disjoint edges.