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Higher connectivity of graph coloring complexes | | Sonja Lj. Cukic
; Dmitry N. Kozlov
; | | Date: |
14 Oct 2004 | | Journal: | IMRN 2005:25 (2005) 1543-1562. | | Subject: | Combinatorics; Algebraic Topology MSC-class: 05C15; 57M15 | math.CO math.AT | | 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 (n-d-2)-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 (n-4)-connected, for $ngeq 3$. | | Source: | arXiv, math.CO/0410335 | | Services: | Forum | Review | PDF | Favorites | |
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