Leafy spanning k-forests

Cristina G. Fernandes (), Carla N. Lintzmayer () and Mário César San Felice ()
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Cristina G. Fernandes: Universidade de São Paulo
Carla N. Lintzmayer: Universidade Federal do ABC
Mário César San Felice: Universidade Federal de São Carlos

Journal of Combinatorial Optimization, 2022, vol. 44, issue 2, No 3, 934-946

Abstract: Abstract We denote by Leafy Spanning $$k$$ 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 $$k=1$$ 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 $$k$$ k -Forest is a 3-approximation based on an approach by Lu and Ravi for the $$k=1$$ k = 1 case. We extend the algorithm of Solis-Oba to achieve a 2-approximation for Leafy Spanning $$k$$ k -Forest.

Keywords: Approximation Algorithms; Maximum Leaf Spanning Tree Problem; Graphs; Spanning Forests; 68W25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-022-00872-z

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