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- W1659608380 abstract "For integers $ngeq 1$, $kgeq 0$, 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 $SG_{n,2}$." @default.
- W1659608380 created "2016-06-24" @default.
- W1659608380 creator A5055368173 @default.
- W1659608380 date "2011-05-23" @default.
- W1659608380 modified "2023-09-25" @default.
- W1659608380 title "Independence Complexes of Stable Kneser Graphs" @default.
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- W1659608380 doi "https://doi.org/10.37236/605" @default.
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