Chromatic roots and minor-closed families of graphs

Thomas Perrett

doi:10.1137/15M1040785

Chromatic roots and minor-closed families of graphs

Thomas Perrett

Department of Applied Mathematics and Computer Science

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Abstract

Given a minor-closed class of graphs G, what is the in mum of the non-trivial roots of the chromatic polynomial of G ε G? When G is the class of all graphs, the answer is known to be 32/27. We answer this question exactly for three minor-closed classes of graphs. Furthermore, we conjecture precisely when the value is larger than 32/27.

Original language	English
Journal	S I A M Journal on Discrete Mathematics
Volume	30
Issue number	3
Pages (from-to)	1883-1897
ISSN	0895-4801
DOIs	https://doi.org/10.1137/15M1040785
Publication status	Published - 2016

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abstract = "Given a minor-closed class of graphs G, what is the in mum of the non-trivial roots of the chromatic polynomial of G ε G? When G is the class of all graphs, the answer is known to be 32/27. We answer this question exactly for three minor-closed classes of graphs. Furthermore, we conjecture precisely when the value is larger than 32/27.",

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Chromatic roots and minor-closed families of graphs

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