Neighborhood Complexes of Stable Kneser Graphs

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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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).

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AMS Subject Classification (2000):

  • 05E99
  • 05C15
  • 05C69
  • 55P15