Higher connectivity of graph coloring complexes

@article{Cukic2004HigherCO,
title={Higher connectivity of graph coloring complexes},
author={Sonja Lj. Cukic and Dmitry N. Kozlov},
journal={International Mathematics Research Notices},
year={2004},
volume={2005},
pages={1543-1562}
}
• Published 14 October 2004
• Mathematics
• International Mathematics Research Notices
The main result of this paper is a proof of the following conjecture of Babson & Kozlov: Theorem. Let G be a graph of maximal valency d, then the complex Hom(G,K_n) is at least (n-d-2)-connected. Here Hom(-,-) denotes the polyhedral complex introduced by Lov\'asz to study the topological lower bounds for chromatic numbers of graphs. We will also prove, as a corollary to the main theorem, that the complex Hom(C_{2r+1},K_n) is (n-4)-connected, for $n\geq 3$.
27 Citations

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