A categorification for the chromatic polynomial

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.

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Keywords

Khovanov homology, graph, chromatic polynomial

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 05C15

References

Forward citations

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)

Laure Helme-Guizon and Yongwu Rong

Abstract