Deciding 4-colorability of planar triangulations

TL;DR

This paper presents a polynomial-time method to determine 4-colorability of planar triangulations by calculating a determinant that counts proper 4-colorings without relying on the Four Color Theorem.

Contribution

It introduces a determinant-based approach to decide 4-colorability of planar triangulations without using the Four Color Theorem.

Findings

Number of proper 4-colorings equals a determinant value

Can efficiently decide if a planar triangulation is 4-colorable

Method operates in polynomial time

Abstract

We show, without using the Four Color Theorem, that for each planar triangulation, the number of its proper vertex colorings by 4 colors is a determinant and thus can be calculated in a polynomial time. In particular, we can efficiently decide if the number is non-zero.