A categorification for the chromatic polynomial

Helme-Guizon, Laure; Rong, Yongwu

doi:10.2140/agt.2005.5.1365

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A categorification for the chromatic polynomial

Laure Helme-Guizon and Yongwu Rong

Algebraic & Geometric Topology 5 (2005) 1365–1388

DOI: 10.2140/agt.2005.5.1365

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

Volume 5, issue 4 (2005)