A categorification for the chromatic polynomial

2004/12/31 by Laure Helme-Guizon, Yongwu Rong · 4 citations
Mathematics · #Advanced Combinatorial Mathematics #Categorification #Chromatic polynomial #Cohomology #Euler characteristic #Exact sequence #Geometric and Algebraic Topology #Graph #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Polynomial #math.CO #math.GT #msc:05C15 #msc:57M27

paper · pdf · doi:10.2140/agt.2005.5.1365

published as Algebr. Geom. Topol. 5 (2005) 1365-1388 · Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-53.abs.html

openalex publication_date 2005/10/14 · arxiv created 2005/10/18 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• CATEGORIFICATION OF THE DICHROMATIC POLYNOMIAL FOR GRAPHS
• A categorification for the Tutte polynomial
• A categorification of the Jones polynomial

Cited by

• On the K-theory of matroids with Tutte coverings
• On the homology theory for the chromatic polynomials
• Tutte's dichromate for signed graphs
• Chromatic polynomial [wikipedia]