Characterization of 4-critical triangle-free toroidal graphs
Combinatorics
2020-09-03 v1
Abstract
We give an exact characterization of 3-colorability of triangle-free graphs drawn in the torus, in the form of 186 "templates" (graphs with certain faces filled by arbitrary quadrangulations) such that a graph from this class is not 3-colorable if and only if it contains a subgraph matching one of the templates. As a consequence, we show every triangle-free graph drawn in the torus with edge-width at least six is 3-colorable, a key property used in an efficient 3-colorability algorithm for triangle-free toroidal graphs.
Keywords
Cite
@article{arxiv.2009.00864,
title = {Characterization of 4-critical triangle-free toroidal graphs},
author = {Zdeněk Dvořák and Jakub Pekárek},
journal= {arXiv preprint arXiv:2009.00864},
year = {2020}
}
Comments
34 pages, 4 figures