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The Hilbert Series of the Clique Complex

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Abstract

For a graph G, we show a theorem that establishes a correspondence between the fine Hilbert series of the Stanley-Reisner ring of the clique complex for the complementary graph of G and the fine subgraph polynomial of G. We obtain from this theorem some corollaries regarding the independent set complex and the matching complex.

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References

  1. Renteln, P.: The Hilbert series of the Face Ring of a Flag Complex. Graphs and Combinatorics 18 (3), 605–619 (2002)

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, V.le Doria, 6 95125, Catania, Italy

    Daniela Ferrarello

  2. Department of Mathematics, Stockholm University, SE, 106 91, Stockholm, Sweden

    Ralf Fröberg

Authors
  1. Daniela Ferrarello
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  2. Ralf Fröberg
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Correspondence to Daniela Ferrarello.

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Ferrarello, D., Fröberg, R. The Hilbert Series of the Clique Complex. Graphs and Combinatorics 21, 401–405 (2005). https://doi.org/10.1007/s00373-005-0634-z

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  • DOI: https://doi.org/10.1007/s00373-005-0634-z

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