a1 North Dakota State University, Fargo, ND 58105
a2 Memphis State University, Memphis, TN 38152
Let k be a positive integer, k ≥ 2. In this paper we study bipartite graphs G such that, for n sufficiently large, each two-coloring of the edges of the complete graph Kn gives a monochromatic copy of G, with some k of its vertices having the maximum degree of these k vertices minus the minimum degree of these k vertices (in the colored Kn) at most k − 2.
(Received March 11 1993)
(Revised July 23 1993)