Four-coloring Eulerian triangulations of the torus
Combinatorics
2024-10-01 v1
Abstract
Hutchinson, Richter and Seymour [J. Combin. Theory Ser. B 84 (2002), 225-239] showed that every Eulerian triangulation of an orientable surface that has a sufficiently high representativity is 4-colorable. We give an explicit bound on the representativity in the case of the torus by proving that every Eulerian triangulation of the torus with representativity at least 10 is 4-colorable. We also observe that the bound on the representativity cannot be decreased to less than 8 as there exists a non-4-colorable Eulerian triangulation of the torus with representativity 7.
Cite
@article{arxiv.2409.19165,
title = {Four-coloring Eulerian triangulations of the torus},
author = {Marcin Brianski and Daniel Kral and Ander Lamaison and Xichao Shu},
journal= {arXiv preprint arXiv:2409.19165},
year = {2024}
}