English

Embedded graph 3-coloring and flows

Combinatorics 2023-03-13 v1 Discrete Mathematics

Abstract

A graph drawn in a surface is a near-quadrangulation if the sum of the lengths of the faces different from 4-faces is bounded by a fixed constant. We leverage duality between colorings and flows to design an efficient algorithm for 3-precoloring-extension in near-quadrangulations of orientable surfaces. Furthermore, we use this duality to strengthen previously known sufficient conditions for 3-colorability of triangle-free graphs drawn in orientable surfaces.

Keywords

Cite

@article{arxiv.2303.05583,
  title  = {Embedded graph 3-coloring and flows},
  author = {Caroline Bang and Zdeněk Dvořák and Emily Heath and Bernard Lidický},
  journal= {arXiv preprint arXiv:2303.05583},
  year   = {2023}
}

Comments

53 pages, 15 figures

R2 v1 2026-06-28T09:10:09.723Z