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A categorification for the chromatic polynomial

Laure Helme-Guizon and Yongwu Rong

Algebraic & Geometric Topology 5 (2005) 1365–1388

arXiv: math.CO/0412264

Abstract

For each graph we construct graded cohomology groups whose graded Euler characteristic is the chromatic polynomial of the graph. We show the cohomology groups satisfy a long exact sequence which corresponds to the well-known deletion-contraction rule. This work is motivated by Khovanov’s work on categorification of the Jones polynomial of knots.

Keywords
Khovanov homology, graph, chromatic polynomial
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 05C15
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Publication
Received: 16 December 2004
Accepted: 11 May 2005
Published: 14 October 2005
Authors
Laure Helme-Guizon
Department of Mathematics
The George Washington University
Washington DC 20052
USA
Yongwu Rong
Department of Mathematics
The George Washington University
Washington DC 20052
USA