Three-coloring triangle-free graphs on surfaces VI. 3-colorability of quadrangulations

TL;DR

This paper presents a linear-time algorithm for determining 3-colorability of quadrangulations on fixed surfaces, enabling efficient coloring and customization of vertex colors.

Contribution

It introduces a novel linear-time algorithm for 3-coloring quadrangulations on fixed surfaces, including vertex color prescriptions.

Findings

Linear-time algorithm for 3-colorability

Applicable to quadrangulations on fixed surfaces

Supports prescribed coloring for limited vertices

Abstract

We give a linear-time algorithm to decide 3-colorability (and find a 3-coloring, if it exists) of quadrangulations of a fixed surface. The algorithm also allows to prescribe the coloring for a bounded number of vertices.