Hyperoctahedral Eulerian idempotents, hodge decompositions, and signed graph coloring complexes

Benjamin Braun; Sarah Crown Rundell

doi:10.37236/3636

Hyperoctahedral Eulerian idempotents, hodge decompositions, and signed graph coloring complexes

Benjamin Braun, Sarah Crown Rundell

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperocta- hedral Eulerian idempotents.

Original language	English
Article number	P2.35
Journal	Electronic Journal of Combinatorics
Volume	21
Issue number	2
DOIs	https://doi.org/10.37236/3636
State	Published - May 22 2014

Keywords

Chromatic polynomial
Coloring complex
Eulerian idempotent
Hodge decomposition
Signed graph

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/3636

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abstract = "Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperocta- hedral Eulerian idempotents.",

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N2 - Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperocta- hedral Eulerian idempotents.

AB - Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperocta- hedral Eulerian idempotents.

KW - Chromatic polynomial

KW - Coloring complex

KW - Eulerian idempotent

KW - Hodge decomposition

KW - Signed graph

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Hyperoctahedral Eulerian idempotents, hodge decompositions, and signed graph coloring complexes

Abstract

Keywords

ASJC Scopus subject areas

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