Authors: Stošić, Marko 
Title: Categorification of the dichromatic polynomial for graphs
Journal: Journal of Knot Theory and its Ramifications
Volume: 17
Issue: 1
First page: 31
Last page: 45
Issue Date: 1-Jan-2008
Rank: M22
ISSN: 0218-2165
DOI: 10.1142/S0218216508005975
For each graph and each positive integer n, we define a chain complex whose graded Euler characteristic is equal to an appropriate n-specialization of the dichromatic polynomial. This also gives a categorification of n-specializations of the Tutte polynomial of graphs. Also, for each graph and integer n ≤ 2, we define the different one-variable n-specializations of the dichromatic polynomial, and for each polynomial, we define graded chain complex whose graded Euler characteristic is equal to that polynomial. Furthermore, we explicitly categorify the specialization of the Tutte polynomial for graphs which corresponds to the Jones polynomial of the appropriate alternating link.
Keywords: Categorification | Chromatic polynomial | Graph | Jones polynomial | Khovanov
Publisher: World Scientific
Project: FCT, Grants no. SFRH/BD/6783/2001 and POCI/MAT/60352/2004

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