Graph Cohomologies from Arbitrary Algebras

2005/06/01 by Laure Helme-Guizon, Helme-Guizon, Laure, Yongwu Rong +1 · 1 citation
Mathematics · #55N35 #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.CO #math.GT #math.QA #msc:55N35

paper · pdf · doi:10.48550/arxiv.math/0506023

18 pages

arxiv created 2005/06/01 · openalex publication_date 2005/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each commutative, graded algebra with finite dimension in each degree, we construct a graded cohomology theory for graphs whose graded Euler characteristic is the chromatic polynomial of the graph. This extends our previous work which was based on the algebra \mathbb Z[x]/(x²).

Cited by

• On the first group of the chromatic cohomology of graphs

Related

• A splitting property of the chromatic homology of the complete graph
• A categorification for the signed chromatic polynomial
• The Graded Classification Conjecture holds for graphs with disjoint cycles
• Reduced chromatic graph cohomology
• Categorification of the Dichromatic Polynomial for Graphs