## Abstract

For integers n ≥ 1, k ≥ 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}.

Original language | English |
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Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Electronic Journal of Combinatorics |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - 2011 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics