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

Engström, Alexander

doi:10.1090/S0002-9939-06-08417-6

A short proof of a conjecture on the connectivity of graph coloring complexes
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Proc. Amer. Math. Soc. 134 (2006), 3703-3705 Request permission

Abstract:

The $\mathtt {Hom}$–complexes were introduced by Lovász to study topological obstructions to graph colorings. It was conjectured by Babson and Kozlov, and proved by Čukić and Kozlov, that $\mathtt {Hom}(G,K_n)$ is $(n-d-2)$–connected, where $d$ is the maximal degree of a vertex of $G$, and $n$ the number of colors. We give a short proof of the conjecture.

References

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