Paths of homomorphisms from stable Kneser graphs

2010/06/02 by Carsten Schultz, Schultz, Carsten
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO

paper · pdf · doi:10.48550/arxiv.1006.0474

7 pages

arxiv created 2010/06/02 · openalex publication_date 2010/06/02 · arxiv updated 2010/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We denote by SG_n,k the stable Kneser graph (Schrijver graph) of stable n-subsets of a set of cardinality 2n+k. For k congruent 3 (mod 4) and n≥2 we show that there is a component of the χ-colouring graph of SG_n,k which is invariant under the action of the automorphism group of SG_n,k. We derive that there is a graph G with χ(G)=χ(SG_n,k) such that the complex Hom(SG_n,k, G) is non-empty and connected. In particular, for k congruent 3 (mod 4) and n≥2 the graph SG_n,k is not a test graph.

Related

• The equivariant topology of stable Kneser graphs
• Independence Complexes of Stable Kneser Graphs
• Shifts of the Stable Kneser Graphs and Hom-Idempotence
• The automorphism group of the s-stable Kneser graphs
• On the neighborhood complex of s-stable Kneser graphs