Maximum k-regular induced subgraphs

Domingos M. Cardoso (), Marcin Kamiński () and Vadim Lozin ()
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Domingos M. Cardoso: Universidade de Aveiro
Marcin Kamiński: RUTCOR—Rutgers University Center for Operations Research
Vadim Lozin: RUTCOR—Rutgers University Center for Operations Research

Journal of Combinatorial Optimization, 2007, vol. 14, issue 4, No 5, 455-463

Abstract: 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.

Keywords: Graphs; Independent sets; Induced matchings; Hamiltonian cycles (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-007-9045-9

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