{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T13:22:52Z","timestamp":1769692972552,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For integers $n\\geq 1$, $k\\geq 0$, the stable Kneser graph $SG_{n,k}$ (also called the Schrijver graph) has as vertex set the stable $n$-subsets of $[2n+k]$ and as edges disjoint pairs of $n$-subsets, where a stable $n$-subset is one that does not contain any $2$-subset of the form $\\{i,i+1\\}$ or $\\{1,2n+k\\}$.  The stable Kneser graphs have been an interesting object of study since the late 1970's when A. Schrijver determined that they are a vertex critical class of graphs with chromatic number $k+2$.  This article contains a study of the independence complexes of $SG_{n,k}$ for small values of $n$ and $k$.  Our contributions are two-fold: first, we prove that the homotopy type of the independence complex of $SG_{2,k}$ is a wedge of spheres of dimension two.  Second, we determine the homotopy types of the independence complexes of certain graphs related to $SG_{n,2}$.<\/jats:p>","DOI":"10.37236\/605","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:47:11Z","timestamp":1578714431000},"source":"Crossref","is-referenced-by-count":10,"title":["Independence Complexes of Stable Kneser Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Benjamin","family":"Braun","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,5,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p118\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p118\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:11:43Z","timestamp":1579302703000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/605","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5,23]]},"article-number":"P118"}}