Polynomial-time algorithm for vertex k-colorability of P_5-free graphs

TL;DR

This paper presents the first polynomial-time algorithm for vertex k-colorability in P_5-free graphs, solving an open problem and extending prior results in graph coloring.

Contribution

It introduces a novel polynomial-time algorithm for k-coloring P_5-free graphs, addressing a longstanding open problem in graph theory.

Findings

Successfully solves the vertex k-colorability problem for P_5-free graphs in polynomial time

Generalizes previous results on graph coloring for specific graph classes

Provides a new approach that can be applied to related graph classes

Abstract

We give the first polynomial-time algorithm for coloring vertices of P_5-free graphs with k colors. This settles an open problem and generalizes several previously known results.