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Maximum k-regular induced subgraphs

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Abstract

Independent sets, induced matchings and cliques are examples of regular induced subgraphs in a graph. In this paper, we prove that finding a maximum cardinality k-regular induced subgraph is an NP-hard problem for any fixed value of k. We propose a convex quadratic upper bound on the size of a k-regular induced subgraph and characterize those graphs for which this bound is attained. Finally, we extend the Hoffman bound on the size of a maximum 0-regular subgraph (the independence number) from k=0 to larger values of k.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Aveiro, 3810-193, Aveiro, Portugal

    Domingos M. Cardoso

  2. RUTCOR—Rutgers University Center for Operations Research, 640 Bartholomew Road, Piscataway, NJ, 08854, USA

    Marcin Kamiński & Vadim Lozin

Authors
  1. Domingos M. Cardoso
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  2. Marcin Kamiński
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  3. Vadim Lozin
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Corresponding author

Correspondence to Domingos M. Cardoso.

Additional information

The first author’s research was supported by Centre for Research on Optimization and Control (CEOC) from the “Fundação para a Ciência e a Tecnologia” FCT, cofinanced by the European Community Fund FEDER/POCI 2010.

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Cardoso, D.M., Kamiński, M. & Lozin, V. Maximum k-regular induced subgraphs. J Comb Optim 14, 455–463 (2007). https://doi.org/10.1007/s10878-007-9045-9

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  • DOI: https://doi.org/10.1007/s10878-007-9045-9

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