On splittable colorings of graphs and hypergraphs
Copyright policy )On splittable colorings of graphs and hypergraphs
AbstractThe notion of a split coloring of a complete graph was introduced by Erdős and Gyárfás [7] as a generalization of split graphs. In this work, 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. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 226–237, 2002
- University of California, San Diego United States
- University of Illinois System United States
- University of Illinois at Urbana Champaign United States
affine plane, Extremal problems in graph theory, Ramsey coloring problem, Generalized Ramsey theory, Hypergraphs, Combinatorial aspects of block designs, Turán theory, group divisible design, split coloring, Coloring of graphs and hypergraphs, complete \(k\)-uniform hypergraph, total colorings, balanced coloring
affine plane, Extremal problems in graph theory, Ramsey coloring problem, Generalized Ramsey theory, Hypergraphs, Combinatorial aspects of block designs, Turán theory, group divisible design, split coloring, Coloring of graphs and hypergraphs, complete \(k\)-uniform hypergraph, total colorings, balanced coloring
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