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A short proof of a conjecture on the higher connectivity of graph coloring complexes

Alexander Engstrom
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Abstract

The Hom-complexes were introduced by Lovasz to study topological obstructions to graph colorings. It was conjectured by Babson and Kozlov, and proved by Cukic and Kozlov, that Hom(G,K_n) is (n-d-2)-connected, where d is the maximal degree of a vertex of G. We give a short proof of the conjecture.

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Alexander Engstrom. 2005-05-22. A short proof of a conjecture on the higher connectivity of graph coloring complexes. https://arxiv.org/abs/math/0505460

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