Algebraic and Geometric Topology 5 (2005), paper no. 53, pages 1365-1388.

A categorification for the chromatic polynomial

Laure Helme-Guizon, Yongwu Rong

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

AMS subject classification. Primary: 57M27. Secondary: 05C15.

E-print: arXiv:math.CO/0412264

DOI: 10.2140/agt.2005.5.1365

Submitted: 16 December 2004. Accepted: 11 May 2005. Published: 14 October 2005.

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Laure Helme-Guizon, Yongwu Rong
Department of Mathematics, The George Washington University
Washington, DC 20052, USA
Email: lhelmeg@yahoo.com, rong@gwu.edu

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