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Maximum k-regular induced subgraphs

Author

Listed:
  • Domingos M. Cardoso

    (Universidade de Aveiro)

  • Marcin Kamiński

    (RUTCOR—Rutgers University Center for Operations Research)

  • Vadim Lozin

    (RUTCOR—Rutgers University Center for Operations Research)

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.

Suggested Citation

  • Domingos M. Cardoso & Marcin Kamiński & Vadim Lozin, 2007. "Maximum k-regular induced subgraphs," Journal of Combinatorial Optimization, Springer, vol. 14(4), pages 455-463, November.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:4:d:10.1007_s10878-007-9045-9
    DOI: 10.1007/s10878-007-9045-9
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    Cited by:

    1. Carlos J. Luz, 2011. "Improving an upper bound on the size of k-regular induced subgraphs," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 882-894, November.

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