Neighborhood complexes of stable Kneser graphs
type: Item
instance of: scholarly article
title: Neighborhood complexes of stable Kneser graphs
zbMATH Open document ID: 1047.05015
published in: Combinatorica
publication date: 2004-09-07T00:00:00Z
review text: The stable Kneser graph \(\mathrm{SG}_{n,k}\) consists of those \(n\)-element subsets of the cyclically ordered set \(\{1,\dots,2n+k\}\) which contain no 2 consecutive elements, with two such \(n\)-sets joined if and only if they are disjoint. It is shown that the neighborhood complex of \(\mathrm{SG}_{n,k}\) is homotopy equivalent to the sphere \({\mathbf S}^k\) for \(n\geq 1\), \(k\geq 0\). The neighborhood complex of \(\mathrm{SG}_{2,k}\) contains, as a deformation retract, the simplicial complex encoding triangulations of a \((k+4)\)-gon.
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05E25
Mathematics Subject Classification ID: 57M15
zbMATH DE Number: 2099002
zbMATH Keywords: neighborhood complexes
zbMATH Keywords: Kneser graphs
author: Anders Bjoerner
author: Mark de Longueville
reviewed by: Péter Komjáth
MaRDI profile type: Publication
full work available at URL: s00493-003-0012-5
OpenAlex ID: W2028850521
DOI: 10.1007/S00493-003-0012-5
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description: scientific article; zbMATH DE number 2099002