Higher connectivity of graph coloring complexes
Abstract
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 (nd2)connected. Here Hom(,) denotes the polyhedral complex introduced by Lovász 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 (n4)connected, for $n\geq 3$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2004
 arXiv:
 arXiv:math/0410335
 Bibcode:
 2004math.....10335C
 Keywords:

 Combinatorics;
 Algebraic Topology;
 05C15;
 57M15
 EPrint:
 16 pages, 6 figures