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Neighborhood Complexes of Stable Kneser Graphs

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It is shown that the neighborhood complexes of a family of vertex critical subgraphs of Kneser graphs—the stable Kneser graphs introduced by L. Schrijver—are spheres up to homotopy. Furthermore, it is shown that the neighborhood complexes of a subclass of the stable Kneser graphs contain the boundaries of associahedra (simplicial complexes encoding triangulations of a polygon) as a strong deformation retract.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S–100 44, Stockholm, Sweden

    Anders Björner*

  2. Freie Universität Berlin, Fachbereich Mathematik, Arnimallee 2-6, 14195, Berlin, Germany

    Mark de Longueville†

Authors
  1. Anders Björner*
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  2. Mark de Longueville†
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Correspondence to Anders Björner*.

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* The first author was partially supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.

† The second author was supported by the graduate school ‘Algorithmische Diskrete Mathematik’, which is funded by the Deutsche Forschungsgemeinschaft, grant GRK 219/3. The DAAD partially supported a stay at KTH, Stockholm, in December 1998, where this work was done: DAAD program AZ 313/S-PPP

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Björner*, A., de Longueville†, M. Neighborhood Complexes of Stable Kneser Graphs. Combinatorica 23, 23–34 (2003). https://doi.org/10.1007/s00493-003-0012-5

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  • DOI: https://doi.org/10.1007/s00493-003-0012-5

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