The chromatic polynomial of fatgraphs and its categorification
By Martin Loebl, Iain Moffatt. 2005
49 citations recorded by the source corpus.
Abstract Motivated by Khovanov homology and relations between the Jones polynomial and graph polynomials, we construct a homology theory for embedded graphs from which the chromatic polynomial can be recovered as the Euler characteristic. For plane graphs, we show that our chromatic homology can be recovered from the Khovanov homology of an associated link. We apply this connection with Khovanov homology to show that the torsion-free part of our chromatic homology is independent of the choice of planar embedding of a graph. We extend our construction and categorify the Bollobas–Riordan polynomial (a generalization of the Tutte polynomial to embedded graphs). We prove that both our chromatic homology and the Khovanov homology of an associated link can be recovered from this categorification.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6949501ab9da87d3ab664fb08bc38a84d253a1bc
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Twisted duality for embedded graphs (2009, result): “In fact, much of our motivation for this study came from recent results relating knots and embedded graphs, and particularly the various recent connections between various realizations of knot polynomials as embedded graph polynomials ([21, 22, 17, 23, 33, 58, 65, 66, 67]).”