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We denote by SGn,k the stable Kneser graph (Schrijver graph) of stable n-subsets of a set of cardinality 2n+k. For k≡3 (mod 4) and n≥2 we show that there is a component of the χ-colouring graph of SGn,k which is invariant under the action of the automorphism group of SGn,k. We derive that there is a graph G with χ(G)=χ(SGn,k) such that the complex Hom(SGn,k,G) is non-empty and connected...
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