Paired- and induced paired-domination in {E,net}-free graphs

• Autorzy: Oliver Schaudt
• Języki publikacji: EN

Abstrakty

EN

A dominating set of a graph is a vertex subset that any vertex belongs to or is adjacent to. Among the many well-studied variants of domination are the so-called paired-dominating sets. A paired-dominating set is a dominating set whose induced subgraph has a perfect matching. In this paper, we continue their study.
We focus on graphs that do not contain the net-graph (obtained by attaching a pendant vertex to each vertex of the triangle) or the E-graph (obtained by attaching a pendant vertex to each vertex of the path on three vertices) as induced subgraphs. This graph class is a natural generalization of {claw, net}-free graphs, which are intensively studied with respect to their nice properties concerning domination and hamiltonicity. We show that any connected {E, net}-free graph has a paired-dominating set that, roughly, contains at most half of the vertices of the graph. This bound is a significant improvement to the known general bounds.
Further, we show that any {E, net, C₅}-free graph has an induced paired-dominating set, that is a paired-dominating set that forms an induced matching, and that such set can be chosen to be a minimum paired-dominating set. We use these results to obtain a new characterization of {E, net, C₅}-free graphs in terms of the hereditary existence of induced paired-dominating sets. Finally, we show that the induced matching formed by an induced paired-dominating set in a {E, net, C₅}-free graph can be chosen to have at most two times the size of the smallest maximal induced matching possible.

Słowa kluczowe

EN

domination; paired-domination; induced paired-domination; induced matchings; {E,net}-free graphs

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 3
• Strony: 473-485

Daty

wydano

2012

otrzymano

2011-03-29

poprawiono

2011-08-31

zaakceptowano

2011-08-31

Twórcy

autor

Oliver Schaudt

• Institut für Informatik, Universität zu Köln, Weyertal 80, 50931 Cologne, Germany

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1617