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arXiv · 2304.13715

Limits of degeneracy for colouring graphs with forbidden minors

Sergey Norin·Jérémie Turcotte
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Abstract

Motivated by Hadwiger's conjecture, Seymour asked which graphs $H$ have the property that every non-null graph $G$ with no $H$ minor has a vertex of degree at most $|V(H)|-2$. We show that for every monotone graph family $\mathcal{F}$ with strongly sublinear separators, all sufficiently large bipartite graphs $H \in \mathcal{F}$ with bounded maximum degree have this property. None of the conditions that $H$ belongs to $\mathcal{F}$, that $H$ is bipartite and that $H$ has bounded maximum degree can be omitted.

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Sergey Norin, Jérémie Turcotte. 2023-04-26. Limits of degeneracy for colouring graphs with forbidden minors. https://doi.org/10.1090/tran%2F9493

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