Size Multipartite Ramsey Numbers for Stripes versus Stripes

Abstract

For graphs \(G\) and \(H\), the size-balanced Ramsey multipartite number \(m_j(G, H)\) is defined as the smallest positive integer \(s\) such that any arbitrary red/blue coloring of the graph \(K_{s,s}\) forces the appearance of a red \(G\) or a blue \(H\). In the main case of this paper, we generalize methods used in finding bipartite Ramsey numbers for \(b(nK_2, mK_2)\) to finding the balanced Ramsey multipartite number \(m_j(nK_2, mK_2)\).