Characterizations of competition multigraphs |
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Authors: | Yoshio Sano |
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Institution: | Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan |
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Abstract: | The notion of a competition multigraph was introduced by C. A. Anderson, K. F. Jones, J. R. Lundgren, and T. A. McKee C. A. Anderson, K. F. Jones, J. R. Lundgren, and T. A. McKee: Competition multigraphs and the multicompetition number, Ars Combinatoria 29B (1990) 185-192] as a generalization of the competition graphs of digraphs.In this note, we give a characterization of competition multigraphs of arbitrary digraphs and a characterization of competition multigraphs of loopless digraphs. Moreover, we characterize multigraphs whose multicompetition numbers are at most m, where m is a given nonnegative integer and give characterizations of competition multihypergraphs. |
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Keywords: | Competition graph Competition multigraph Competition hypergraph Multicompetition number Edge clique partition |
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