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- W4300536430 abstract "In this paper, we consider multivariate hyperedge elimination polynomials and multivariate chromatic polynomials for hypergraphs. The first set of polynomials is defined in terms of a deletion-contraction-extraction recurrence, previously investigated for graphs by Averbouch, Godlin, and Makowsky. The multivariate chromatic polynomial is an equivalent polynomial defined in terms of colorings, and generalizes the coboundary polynomial of Crapo, and the bivariate chromatic polynomial of Dohmen, Ponitz and Tittman. We show that specializations of these new polynomials recover polynomials which enumerate hyperedge coverings, matchings, transversals, and section hypergraphs. We also prove that the polynomials can be defined in terms of Mobius inversion on the bond lattice of a hypergraph, as well as compute these polynomials for various classes of hypergraphs." @default.
- W4300536430 created "2022-10-03" @default.
- W4300536430 creator A5074579366 @default.
- W4300536430 date "2010-12-15" @default.
- W4300536430 modified "2023-09-28" @default.
- W4300536430 title "On Multivariate Chromatic Polynomials of Hypergraphs and Hyperedge Elimination" @default.
- W4300536430 doi "https://doi.org/10.48550/arxiv.1012.3423" @default.
- W4300536430 hasPublicationYear "2010" @default.
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