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Paired-Domination in Subdivided Star-Free Graphs

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Abstract

A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G, denoted by γ pr(G), is the minimum cardinality of a paired-dominating set of G. In [Dorbec P, Gravier S, Henning MA, J Comb Optim 14(1):1–7, 2007], the authors gave tight bounds for paired-dominating sets of generalized claw-free graphs. Yet, the critical cases are not claws but subdivided stars. We here give a bound for graphs containing no induced subdivided stars, depending on the size of the star.

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Authors and Affiliations

  1. LaBRI, Université Bordeaux 1, 351 cours de la Libération, 33405, Talence, France

    Paul Dorbec

  2. ERTÉ “Maths à modeler”, Institut Fourier, BP 74, 100 rue des maths, 38402, St. Martin d’Hères Cedex, France

    Sylvain Gravier

Authors
  1. Paul Dorbec
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  2. Sylvain Gravier
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Correspondence to Paul Dorbec.

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Dorbec, P., Gravier, S. Paired-Domination in Subdivided Star-Free Graphs. Graphs and Combinatorics 26, 43–49 (2010). https://doi.org/10.1007/s00373-010-0893-1

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  • DOI: https://doi.org/10.1007/s00373-010-0893-1

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