|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||Abstract:||
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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