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A new characterization of P6-free graphs.

By P. van 't Hof and Daniel Paulusma

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.\ud \u

Topics: Paths, Cycles, Induced subgraphs, Complete bipartite graph, Dominating set, Computational complexity.
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.dam.2008.08.025
OAI identifier: oai:dro.dur.ac.uk.OAI2:7417
Journal:

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