Properties of 8-contraction-critical graphs with no K7 minor
Department
Mathematics
Document Type
Article
Publication Date
5-1-2023
Abstract
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.
Journal Title
European Journal of Combinatorics
Journal ISSN
01956698
Volume
110
Digital Object Identifier (DOI)
10.1016/j.ejc.2023.103711
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