Authors: Stošić, Marko 
Title: New categorifications of the chromatic and dichromatic polynomials for graphs
Journal: Fundamenta Mathematicae
Volume: 190
First page: 231
Last page: 243
Issue Date: 5-Jul-2006
Rank: M22
ISSN: 0016-2736
DOI: 10.4064/fm190-0-9
Abstract: 
For each graph G, we define a chain complex of graded modules over the ring of polynomials whose graded Euler characteristic is equal to the chromatic polynomial of G. Furthermore, we define a chain complex of doubly-graded modules whose (doubly) graded Euler characteristic is equal to the dichromatic polynomial of G. Both constructions use Koszul complexes, and are similar to the new Khovanov-Rozansky categorifications of the HOMFLYPT polynomial. We also give a simplified definition of this triply-graded link homology theory.
Keywords: Chromatic polynomial | Dichromatic polynomial | Graph | Homology | Khovanov-Rozansky | Koszul complex
Publisher: Instytut Matematyczny Polskiej Akademii Nauk
Project: FCT, Grant no. SFRH/BD/6783/2001

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