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arXiv · 2504.07764

A note on extendable sets of colorings and rooted minors

Zdeněk Dvořák·Jan M. Swart
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Abstract

DeVos and Seymour (2003) proved that for every set $C$ of 3-colorings of a set $X$ of vertices, there exists a plane graph $G$ with vertices of $X$ incident with the outer face such that a 3-coloring of $X$ extends to a 3-coloring of $G$ if and only if it belongs to $C$. We prove a generalization of this claim for $k$-colorings of $X$-rooted-$K_{k+1}$-minor-free $K_{k+2}$-minor-free graphs.

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Zdeněk Dvořák, Jan M. Swart. 2025-04-10. A note on extendable sets of colorings and rooted minors. https://arxiv.org/abs/2504.07764

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