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Leafy spanning k-forests

Author

Listed:
  • Cristina G. Fernandes

    (Universidade de São Paulo)

  • Carla N. Lintzmayer

    (Universidade Federal do ABC)

  • Mário César San Felice

    (Universidade Federal de São Carlos)

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.

Suggested Citation

  • Cristina G. Fernandes & Carla N. Lintzmayer & Mário César San Felice, 2022. "Leafy spanning k-forests," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 934-946, September.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:2:d:10.1007_s10878-022-00872-z
    DOI: 10.1007/s10878-022-00872-z
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