A new characterization of P6-free graphs

Hof, P. van't; Paulusma, D.

Abstract

We study P 6-free graphs, i.e., graphs that do not contain an induced path on six vertices. Our main result is a new characterization of this graph class: a graph G is P 6-free if and only if each connected induced subgraph of G on more than one vertex contains a dominating induced cycle on six vertices or a dominating (not necessarily induced) complete bipartite subgraph. This characterization is minimal in the sense that there exists an infinite family of P 6-free graphs for which a smallest connected dominating subgraph is a (not induced) complete bipartite graph. Our characterization of P 6-free graphs strengthens results of Liu and Zhou, and of Liu, Peng and Zhao. Our proof has the extra advantage of being constructive: we present an algorithm that finds such a dominating subgraph of a connected P 6-free graph in polynomial time. This enables us to solve the Hypergraph 2-Colorability problem in polynomial time for the class of hypergraphs with P 6-free incidence graphs.

Citation

Hof, P. V., & Paulusma, D. (2008, December). A new characterization of P6-free graphs. Presented at 14th Annual International Computing and Combinatorics Conference, Dalian, China

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 14th Annual International Computing and Combinatorics Conference
• Publication Date: Jun 1, 2008
• Deposit Date: Oct 6, 2010
• Print ISSN: 0302-9743
• Pages: 415-424
• Series Title: Lecture notes in computer science
• Series Number: 5092
• Series ISSN: 0302-9743,1611-3349
• Edition: 14th ed.
• Book Title: Computing and combinatorics, 14th Annual International Conference, COCOON 2008, 27-29 June 2008 Dalian, China ; proceedings.
• DOI: https://doi.org/10.1007/978-3-540-69733-6_41
• Public URL: https://durham-repository.worktribe.com/output/1159279