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Leafy spanning k-forests

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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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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  • DOI: https://doi.org/10.1007/s10878-022-00872-z

Keywords

  • Approximation Algorithms
  • Maximum Leaf Spanning Tree Problem
  • Graphs
  • Spanning Forests

Mathematics Subject Classification

  • 68W25