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A new characterization of P6-free graphs.

Hof, P. van 't and Paulusma, Daniel (2010) 'A new characterization of P6-free graphs.', Discrete applied mathematics., 158 (7). pp. 731-740.


We study P6-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 P6-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 P6-free graphs for which a smallest connected dominating subgraph is a (not induced) complete bipartite graph. Our characterization of P6-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 P6-free graph in polynomial time. This enables us to solve the Hypergraph 2-Colorability problem in polynomial time for the class of hypergraphs with P6-free incidence graphs.

Item Type:Article
Keywords:Paths, Cycles, Induced subgraphs, Complete bipartite graph, Dominating set, Computational complexity.
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Publisher statement:NOTICE: this is the author's version of a work that was accepted for publication in Discrete applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete applied mathematics, 158/7, 6 April 2010, 10.1016/j.dam.2008.08.025
Date accepted:No date available
Date deposited:07 October 2010
Date of first online publication:April 2010
Date first made open access:No date available

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