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Matching Trees for Simplicial Complexes and Homotopy Type of Devoid Complexes of Graphs

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Abstract

We generalize some homotopy calculation techniques such as splittings and matching trees that are introduced for the computations in the case of the independence complexes of graphs to arbitrary simplicial complexes. We then exemplify their efficiency on some simplicial complexes, the devoid complexes of graphs, \(\mathcal {D}(G;\mathcal {F})\) whose faces are vertex subsets of G that induce \(\mathcal {F}\)-free subgraphs, where G is a multigraph and \(\mathcal {F}\) is a family of multigraphs. Additionally, we compute the homotopy type of dominance complexes of chordal graphs.

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Authors and Affiliations

  1. Department of Mathematics, University Of Bremen, 28359, Bremen, Germany

    Demet Taylan

  2. Department of Mathematics, Bozok University, 66200, Yozgat, Turkey

    Demet Taylan

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  1. Demet Taylan
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Correspondence to Demet Taylan.

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The author is supported by TÜBİTAK, grant no: 111T704.

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Taylan, D. Matching Trees for Simplicial Complexes and Homotopy Type of Devoid Complexes of Graphs. Order 33, 459–476 (2016). https://doi.org/10.1007/s11083-015-9379-3

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  • DOI: https://doi.org/10.1007/s11083-015-9379-3

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