Properties of 8-contraction-critical graphs with no K7 minor

Motivated by the famous Hadwiger’s Conjecture, we study the properties of 8-contraction-critical graphs with no K7 minor. In particular, we prove that every 8-contraction-critical graph with no K7 minor has at most one vertex of degree 8, where a graph G is 8-contraction-critical if G is not 7-color...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 110
Main Authors Rolek, Martin, Song, Zi-Xia, Thomas, Robin
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2023
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Summary:Motivated by the famous Hadwiger’s Conjecture, we study the properties of 8-contraction-critical graphs with no K7 minor. In particular, we prove that every 8-contraction-critical graph with no K7 minor has at most one vertex of degree 8, where a graph G is 8-contraction-critical if G is not 7-colorable but every proper minor of G is 7-colorable. This is one step in our effort to prove that every graph with no K7 minor is 7-colorable, which remains open.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2023.103711