A categorification for the chromatic polynomial

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-53.abs.html

References in corpus (2)

• Matrix factorizations and link homology II
• A categorification for the Tutte polynomial

Cited by in corpus (10)

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• Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology
• The homology of digraphs as a generalisation of Hochschild homology
• Multipath cohomology of directed graphs
• Khovanov homology and star-like isotopies
• On finite generation in magnitude (co)homology, and its torsion