A new characterization of P6-free graphs

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

doi:10.1016/j.dam.2008.08.025

A new characterization of P6-free graphs

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

Authors

P. van 't Hof

Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor

Contributors

Pim van 't Hof dcs3pv@durham.ac.uk
Other

Abstract

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.

Citation

Hof, P. V. '., & Paulusma, D. (2010). A new characterization of P6-free graphs. Discrete Applied Mathematics, 158(7), 731-740. https://doi.org/10.1016/j.dam.2008.08.025

Journal Article Type	Article
Publication Date	Apr 6, 2010
Deposit Date	Oct 6, 2010
Publicly Available Date	Oct 7, 2010
Journal	Discrete Applied Mathematics
Print ISSN	0166-218X
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	158
Issue	7
Pages	731-740
DOI	https://doi.org/10.1016/j.dam.2008.08.025
Keywords	Paths, Cycles, Induced subgraphs, Complete bipartite graph, Dominating set, Computational complexity.
Public URL	https://durham-repository.worktribe.com/output/1517209

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Copyright 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