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Leafy spanning k-forests

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Abstract

We denote by Leafy  Spanning \(k\)-Forest the problem of, given a positive integer k and a graph G with at most k components, finding a spanning forest in G with at most k components and the maximum number of leaves. The case \(k=1\) is known to be NP-hard, and is well studied in the literature, with the best approximation algorithm having been proposed more than 20 years ago by Solis-Oba. The best approximation algorithm known for Leafy  Spanning \(k\)-Forest is a 3-approximation based on an approach by Lu and Ravi for the \(k=1\) case. We extend the algorithm of Solis-Oba to achieve a 2-approximation for Leafy  Spanning \(k\)-Forest.

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Funding

C. G. Fernandes was partially supported by the National Council for Scientific and Technological Development – CNPq (Proc. 310979/2020-0 and 423833/2018-9). C. N. Lintzmayer was partially supported by CNPq (Proc. 312026/2021-8 and 428385/2018-4). This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

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Authors and Affiliations

  1. Departamento de Ciência da Computação, Universidade de São Paulo, São Paulo, Brazil

    Cristina G. Fernandes

  2. Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André, Brazil

    Carla N. Lintzmayer

  3. Departamento de Computação, Universidade Federal de São Carlos, São Carlos, Brazil

    Mário César San Felice

Authors
  1. Cristina G. Fernandes
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  2. Carla N. Lintzmayer
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  3. Mário César San Felice
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Correspondence to Carla N. Lintzmayer.

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Fernandes, C.G., Lintzmayer, C.N. & San Felice, M.C. Leafy spanning k-forests. J Comb Optim 44, 934–946 (2022). https://doi.org/10.1007/s10878-022-00872-z

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