Geodesic
A categorification for the chromatic polynomial
Helme-Guizon, Laure1 ; Rong, Yongwu1
1Department of Mathematics, The George Washington University, Washington DC 20052, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1365-1388
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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.

DOI : 10.2140/agt.2005.5.1365
Keywords: Khovanov homology, graph, chromatic polynomial

Helme-Guizon, Laure  1   ; Rong, Yongwu  1

1 Department of Mathematics, The George Washington University, Washington DC 20052, USA 
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Helme-Guizon, Laure; Rong, Yongwu. A categorification for the chromatic polynomial. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1365-1388. doi: 10.2140/agt.2005.5.1365

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