English

3-coloring triangle-free planar graphs with a precolored 9-cycle

Combinatorics 2017-09-28 v1

Abstract

Given a triangle-free planar graph G and a 9-cycle C in G, we characterize situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous results when C is a cycle of length at most 8.

Keywords

Cite

@article{arxiv.1709.09428,
  title  = {3-coloring triangle-free planar graphs with a precolored 9-cycle},
  author = {Ilkyoo Choi and Jan Ekstein and Přemysl Holub and Bernard Lidický},
  journal= {arXiv preprint arXiv:1709.09428},
  year   = {2017}
}

Comments

38 pages, 19 figures

R2 v1 2026-06-22T21:56:27.075Z