On List Colouring and List Homomorphism of Permutation and Interval Graphs

TL;DR

This paper presents polynomial-time algorithms for list colouring and list homomorphism problems on permutation and interval graphs, which are generally NP-complete, thus advancing efficient solutions for these graph classes.

Contribution

The paper introduces polynomial-time algorithms for list colouring and list homomorphism on permutation and interval graphs, extending tractability results to these classes.

Findings

Polynomial-time algorithm for list colouring permutation graphs with bounded colours

Polynomial-time solution for list-homomorphism problems on permutation and interval graphs

Extension of tractability to a large class of input graphs including all permutation and interval graphs

Abstract

List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded total number of colours. More generally we give a polynomial-time algorithm that solves the list-homomorphism problem to any fixed target graph for a large class of input graphs including all permutation and interval graphs.