The Ramsey Numbers \(r(mC_4, nC_5)\)

If \(G\) and \(H\) are graphs, define the Ramsey number \(r(G, H)\) to be the least number \(p\) such that if the edges of the complete graph \(K_p\) are colored red and blue (say), either the red graph contains a copy of \(G\), or the blue graph contains a copy of \(H\). In this paper, we determine the Ramsey number \(r(mC_4, nC_5)\) for any \(m\geq1, n\geq1\).