k-Colorability of P5-free graphs

TL;DR

This paper presents a polynomial-time algorithm for determining whether P5-free graphs can be colored with k colors, and constructs such a coloring if it exists, advancing graph coloring theory for this class.

Contribution

The paper introduces the first polynomial-time algorithm for k-coloring P5-free graphs, providing both decision and construction capabilities.

Findings

Polynomial-time algorithm for k-coloring P5-free graphs

Algorithm produces valid k-coloring if it exists

Advances understanding of graph coloring in P5-free graphs

Abstract

A polynomial time algorithm that determines for a fixed integer k whether or not a P5-free graph can be k-colored is presented in this paper. If such a coloring exists, the algorithm will produce a valid k-coloring.