Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs

Huang, S.; Johnson, M.; Paulusma, D.

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).

Citation

Huang, S., Johnson, M., & Paulusma, D. (2014, December). Narrowing the Complexity Gap for Colouring (C_s,P_t)-Free Graphs. Presented at 10th International Conference, AAIM 2014, Vancouver, BC, Canada

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 10th International Conference, AAIM 2014
• Publication Date: Jan 1, 2014
• Deposit Date: Dec 20, 2014
• Publicly Available Date: Jan 15, 2015
• Print ISSN: 0302-9743
• Pages: 162-173
• Series Title: Lecture notes in computer science
• Series Number: 8546
• Series ISSN: 0302-9743,1611-3349
• Book Title: 10th International Conference, AAIM 2014, Vancouver, BC, Canada, 8-11 July 2014 ; proceedings.
• ISBN: 978-3-319-07955-4
• DOI: https://doi.org/10.1007/978-3-319-07956-1_15
• Public URL: https://durham-repository.worktribe.com/output/1154476