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- W2897501026 abstract "In 1978, László Lovász proved the famous Kneser Conjecture – concerning the chromatic number of the Kneser graphs KGm,n – introducing the neighborhood complex. In the same year, Alexander Schrijver defined certain induced subgraphs of KGm,n – called the stable Kneser graphs SGm,n – and showed that they are vertex-critical. Schrijver used another, Bárány’s method to obtain the chromatic number of the stable Kneser graphs. Almost 25 years later, in 2002, Anders Björner and Mark de Longueville studied the neighborhood complex of SGm,n, and determined the homotopy type of them. Frédéric Meunier generalized Schrijver’s construction and formulated the conjecture on the chromatic number of the s-stable and almost s-stable Kneser graphs. We shall determine the homotopy type of the neighborhood complex of the almost s-stable Kneser graphs. In conjunction with Lovász’s topological bound on the chromatic number, we give the chromatic number of these graphs, which was recently determined by Chen using other methods." @default.
- W2897501026 created "2018-10-26" @default.
- W2897501026 creator A5022862693 @default.
- W2897501026 date "2019-02-01" @default.
- W2897501026 modified "2023-10-18" @default.
- W2897501026 title "The neighborhood complexes of almost <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll id=d1e436 altimg=si8.gif><mml:mi>s</mml:mi></mml:math>-stable Kneser graphs" @default.
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- W2897501026 doi "https://doi.org/10.1016/j.ejc.2018.09.002" @default.
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