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{\bf Benjamin Braun}
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{\bf Independence Complexes of Stable Kneser Graphs}
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For integers $n\geq 1$, $k\geq 0$, the \emph{stable Kneser graph}
$SG_{n,k}$ (also called the \emph{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 $SG_{n,2}$.
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