We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

A new characterization of P6-free graphs.

Hof, P. van 't and Paulusma, Daniel (2008) 'A new characterization of P6-free graphs.', in Computing and combinatorics, 14th Annual International Conference, COCOON 2008, 27-29 June 2008 Dalian, China ; proceedings. Berlin ; Heidelberg: Springer, pp. 415-424. Lecture notes in computer science. (5092).


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.

Item Type:Book chapter
Full text:Full text not available from this repository.
Publisher Web site:
Record Created:07 Oct 2010 12:35
Last Modified:24 Aug 2016 09:28

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Look up in GoogleScholar | Find in a UK Library