A Note on Multicolor Bipartite Ramsey Numbers for \(K_{2,n}\)

Abstract

In this note we prove that the bipartite Ramsey number for \(K_{2,n}\) with \(q\) colors does not exceed \((n-1)q^2+q+1-\left\lceil\sqrt{q}\right\rceil\), improving the previous upper bound by \(\left\lceil\sqrt{q}\right\rceil-2\).