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Dominating cliques in P5-free graphs

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Abstract

All induced connected subgraphs of a graphG contain a dominating set of pair-wise adjacent vertices if and only if there is no induced subgraph isomorphic to a path or a cycle of five vertices inG. Moreover, the problem of finding any given type of connected dominating sets in all members of a classG of graphs can be reduced to the graphsG∈G that have a cut-vertex or do not contain any cutsetS dominated by somes∈S.

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Authors and Affiliations

  1. Köztársaság Tér 1, H-1081, Budapest, Hungary

    G. Bacsó & Zs. Tuza

  2. Computer and Automation, Institute Hungarian Academy of Sciences, Kende U. 13-17, H-1111, Budapest, Hungary

    G. Bacsó & Zs. Tuza

Authors
  1. G. Bacsó
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  2. Zs. Tuza
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Additional information

This research was supported in part by the “AKA” Research Fund of the Hungarian Academy of Sciences.

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Bacsó, G., Tuza, Z. Dominating cliques in P5-free graphs. Period Math Hung 21, 303–308 (1990). https://doi.org/10.1007/BF02352694

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  • DOI: https://doi.org/10.1007/BF02352694

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