A remark on the Whitney Broken Circuit Theorem

Aldo Procacci; Emanuel Juliano; Paula M. S. Fialho

A remark on the Whitney Broken Circuit Theorem

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arxiv 2407.04035 v1 pith:MJ7SNRP7 submitted 2024-07-04 math.CO

Paula M. S. Fialho , Emanuel Juliano , Aldo Procacci This is my paper · ORCID

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In the present note we show, via the connection between chromatic polynomial and Potts model, that the Whitney Broken circuit theorem is in fact a special case of a more general identity relating the chromatic polynomial of a graph G=(V,E) to sums over forests of G associated to some partition scheme in G.

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On the independent set polynomial of graphs and claw-free graphs
math.CO 2025-05 conditional novelty 5.0 of 10

For claw-free graphs, the independence polynomial is proven zero-free in a disk of radius at least 1/(2Delta+1), beating Shearer's radius for degree at least 4, and a new signed forest-sum identity for the polynomial ...

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