# Narrowing the Complexity Gap for Colouring (Cs,Pt)-Free Graphs

• Shenwei Huang
• Matthew Johnson
• Daniël Paulusma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)

## Abstract

Let k be a positive integer. The k-Colouring problem is to decide whether a graph has a k-colouring. The k-Precolouring Extension problem is to decide whether a colouring of a subset of a graph’s vertex set can be extended to a k-colouring of the whole graph. A k-list assignment of a graph is an allocation of a list — a subset of {1,…,k} — to each vertex, and the List k -Colouring problem asks whether the graph has a k-colouring in which each vertex is coloured with a colour from its list. We prove a number of new complexity results for these three decision problems when restricted to graphs that do not contain a cycle on s vertices or a path on t vertices as induced subgraphs (for fixed positive integers s and t).

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© Springer International Publishing Switzerland 2014

## Authors and Affiliations

• Shenwei Huang
• 1
• Matthew Johnson
• 2
• Daniël Paulusma
• 2
1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
2. 2.School of Engineering and Computing SciencesDurham University, Science LaboratoriesDurhamUnited Kingdom