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|
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|Publisher Web site:||http://dx.doi.org/10.1007/978-3-540-69733-6_41|
|Record Created:||07 Oct 2010 12:35|
|Last Modified:||24 Aug 2016 09:28|
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