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Discrete Morse Theory and the Homotopy Type of Clique Graphs

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Abstract

We attach topological concepts to a simple graph by means of the simplicial complex of its complete subgraphs. Using Forman’s discrete Morse theory we show that the strong product of two graphs is homotopic to the topological product of the spaces of their complexes. As a consequence, we enlarge the class of clique divergent graphs known to be homotopy equivalent to all its iterated clique graphs.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, México, 04510 D.F., Mexico

    F. Larrión

  2. Depto. de Ingeniería Eléctrica, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco186, Col Vicentina, México, 09340 D.F., Mexico

    M. A. Pizaña

  3. Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, Carr. Pachuca-Tulancingo km. 4.5, Pachuca, 42184 Hgo., Mexico

    R. Villarroel-Flores

Authors
  1. F. Larrión
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  2. M. A. Pizaña
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  3. R. Villarroel-Flores
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Correspondence to R. Villarroel-Flores.

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Partially supported by SEP-CONACyT, grant 183210.

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Larrión, F., Pizaña, M.A. & Villarroel-Flores, R. Discrete Morse Theory and the Homotopy Type of Clique Graphs. Ann. Comb. 17, 743–754 (2013). https://doi.org/10.1007/s00026-013-0204-7

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  • DOI: https://doi.org/10.1007/s00026-013-0204-7

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