Properties of $8$-contraction-critical graphs with no $K_7$ minor
Combinatorics
2022-08-23 v2
Abstract
Motivated by the famous Hadwiger's Conjecture, we study the properties of -contraction-critical graphs with no minor; we prove that every -contraction-critical graph with no minor has at most one vertex of degree , where a graph is -contraction-critical if is not -colorable but every proper minor of is -colorable. This is one step in our effort to prove that every graph with no minor is -colorable, which remains open.
Cite
@article{arxiv.2208.07335,
title = {Properties of $8$-contraction-critical graphs with no $K_7$ minor},
author = {Martin Rolek and Zi-Xia Song and Robin Thomas},
journal= {arXiv preprint arXiv:2208.07335},
year = {2022}
}