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

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

2005-05-22

arxiv.org/abs/math/0505460v1

Mathematics

Combinatorics

3 pages

Scientific paper

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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