Centered colorings in minor-closed graph classes
J\k{e}drzej Hodor, Hoang La, Piotr Micek, Cl\'ement Rambaud

TL;DR
This paper proves that for any fixed minor-closed graph class excluding a complete graph, there exists a bounded-coloring scheme called p-centered coloring, with the number of colors depending polynomially on p and the size of the excluded minor.
Contribution
It establishes a polynomial bound on the number of colors needed for p-centered colorings in K_t-minor-free graphs, extending understanding of colorings in minor-closed classes.
Findings
K_t-minor-free graphs admit p-centered colorings with O(p^{t-1}) colors
The result generalizes previous bounds for specific minor-closed classes
Provides a new tool for graph coloring in minor-closed graph classes
Abstract
A vertex coloring of a graph is -centered if for every connected subgraph of , either uses more than colors on , or there is a color that appears exactly once on . We prove that for every fixed positive integer , every -minor-free graph admits a -centered coloring using colors.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
