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- W3122156687 abstract "In 2002, Björner and de Longueville showed the neighborhood complex of the 2-stable Kneser graph KG(n,k)2−stab has the same homotopy type as the (n−2k)-sphere. A short time ago, an analogous result about the homotopy type of the neighborhood complex of almost s-stable Kneser graph has been announced by the second author. Combining this result with the famous Lovász’s topological lower bound on the chromatic number of graphs yielded a new way for determining the chromatic number of these graphs which was determined a bit earlier by Chen. In this paper we present a common generalization of the mentioned results. For given an integer vector s→=(s1,…,sk), first we define s→-stable Kneser graph KG(n,k)s→−stab as an induced subgraph of the Kneser graph KG(n,k). Then, we show that the neighborhood complex of KG(n,k)s→−stab has the same homotopy type as the n−∑i=1k−1si−2-sphere for some specific values of the parameter s→. In particular, this implies that χKG(n,k)s→−stab=n−∑i=1k−1si for those parameters. Moreover, as a simple corollary of this result, we give a lower bound on the chromatic number of 3-stable Kneser graphs which is just one less than the number conjectured in this regard." @default.
- W3122156687 created "2021-02-01" @default.
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- W3122156687 date "2021-04-01" @default.
- W3122156687 modified "2023-10-04" @default.
- W3122156687 title "On the neighborhood complex of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e22 altimg=si12.svg><mml:mover accent=true><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover></mml:math>-stable Kneser graphs" @default.
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- W3122156687 doi "https://doi.org/10.1016/j.disc.2021.112302" @default.
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