Classifying k-Edge Colouring for H-free Graphs

TL;DR

This paper investigates the computational complexity of the k-Edge Colouring problem within H-free graphs, providing a comprehensive classification based on the structure of H.

Contribution

It offers a complete complexity classification of k-Edge Colouring for H-free graphs, extending understanding of graph coloring problems.

Findings

Complexity results for various H-free graph classes

Identification of cases where k-Edge Colouring is polynomial-time solvable

Identification of cases where k-Edge Colouring is NP-complete

Abstract

A graph is $H$-free if it does not contain an induced subgraph isomorphic to $H$. For every integer $k$ and every graph $H$, we determine the computational complexity of $k$-Edge Colouring for $H$-free graphs.