Reduced chromatic graph cohomology

2005/10/26 by Michael Chmutov, Chmutov, Michael, Elena Udovina +1
Mathematics · #05C15 #57M27 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CO #math.GT #msc:05C15 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0510536

11 pages, 1 figure

arxiv created 2005/10/26 · openalex publication_date 2005/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a new characterization of the h-vector of the chromatic polynomial of a graph. We introduce reduced chromatic cohomology of a graph and show that h_i are its Betti numbers. We then discuss various combinatorial properties of these cohomologies. In particular we prove that these cohomologies depend only on the matroid type of the graph and describe their relationship to the regular chromatic cohomologies.

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