$5$-list-coloring toroidal $6$-regular triangulations in linear time

TL;DR

This paper presents a linear-time algorithm for 5-list-coloring a broad class of toroidal 6-regular triangulations and proves these graphs are not 3-choosable, advancing understanding of graph coloring complexities.

Contribution

It introduces an explicit linear-time coloring procedure for certain toroidal graphs and establishes non-3-choosability, filling gaps in graph coloring theory.

Findings

Linear-time 5-list-coloring algorithm for specified toroidal graphs

Proof that these graphs are not 3-choosable

Enhanced understanding of coloring constraints in toroidal triangulations

Abstract

We give an explicit procedure for $5$-list-coloring a large class of toroidal $6$-regular triangulations in linear time. We also show that these graphs are not $3$-choosable.