A Proof of a Conjecture on Bipartite Ramsey Numbers B(2,2,3)

Abstract

The bipartite Ramsey number B(n1,n2,…,nt) is the least positive integer b, such that any coloring of the edges of Kb,b with t colors will result in a monochromatic copy of Kni,ni in the i-th color, for some i, 1≤i≤t. The values B(2,5)=17, B(2,2,2,2)=19 and B(2,2,2)=11 have been computed in several previously published papers. In this paper, we obtain the exact values of the bipartite Ramsey number B(2,2,3). In particular, we prove the conjecture on B(2,2,3) which was proposed in 2015—in fact, we prove that B(2,2,3)=17.