A categorification for the chromatic polynomial

By Laure Helme-Guizon, Yongwu Rong. 2004

83 citations recorded by the source corpus.

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 corre- sponds to the well-known deletion-contraction rule. This work is motivated by Khovanov's work on categorification of the Jones polynomial of knots. AMS Classification 57M27; 05C15

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21c482d67f783bf5fa3a625ea84d5d57d4c94b5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Iain Moffatt
2. Richard Hepworth
3. Martin Loebl
4. Simon Willerton
5. Tom Leinster
6. Michael Shulman

In Geometry and Topology

1. Richard Hepworth
2. Iain Moffatt
3. Martin Loebl
4. Simon Willerton
5. Tom Leinster
6. Michael Shulman

In Mathematical Physics

1. Richard Hepworth
2. Iain Moffatt
3. Martin Loebl
4. Simon Willerton

Citations in the corpus

• The chromatic polynomial of fatgraphs and its categorification (2005, background): “We prove that both our chromatic homology and the Khovanov homology of an associated link can be recovered from this categorification.”
• Categorifying the magnitude of a graph (2015, methodology): “Thus our categorification is in exactly the same spirit as existing categorifications of polynomial invariants in knot theory and graph theory, for example Khovanov’s categorification of the Jones polynomial [6], Ozsvath-Szabo’s categorification of the Alexander polynomial [17], Helme-Guizon and Ron”