On the Ramsey numbers r(K2,n-1, K2,n) and r(K2,n, K2,n)

Abstract

An upper bound on the Ramsey number r(K_2,n-1, K_2,n) is presented. By constructing a special (K_2,n-1, K_2,n)_4n-5-coloring from symmetric Hadamard matrices we prove that this bound matches the exact value of r(K_2,n-1, K_2,n) in infinitely many cases including all but four n ≤ 58. Moreover, some results on the diagonal Ramsey number r(K_2,n, K_2,n) extending those in [1] are given.