On splittable colorings of graphs and hypergraphs

The notion of a split coloring of a complete graph was introduced by Erdős and Gyárfás [7] as a generalization of split graphs. In this paper, we offer an alternate interpretation by comparing such a coloring to the classical Ramsey coloring problem via a two-round game played against an adversary. We show that the techniques used and bounds obtained on the extremal (r,m)-split coloring problem of [7] are closer in nature to the Turán theory of graphs rather than Ramsey theory. We extend the notion of these colorings to hypergraphs and provide bounds and some exact results. c © (Year) John Wiley & Sons, Inc.