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On some hard and some tractable cases of the maximum acyclic matching problem

Author

Listed:
  • M. Fürst

    (Ulm University)

  • D. Rautenbach

    (Ulm University)

Abstract

Three well-studied types of subgraph-restricted matchings are induced matchings, uniquely restricted matchings, and acyclic matchings. While it is hard to determine the maximum size of a matching of each of these types, whether some given graph has a maximum matching that is induced or has a maximum matching that is uniquely restricted, can both be decided efficiently. In contrast to that we show that deciding whether a given bipartite graph of maximum degree at most four has a maximum matching that is acyclic is NP-complete. Furthermore, we show that maximum weight acyclic matchings can be determined efficiently for $$P_4$$ P 4 -free graphs and $$2P_3$$ 2 P 3 -free graphs, and we characterize the graphs for which every maximum matching is acyclic.

Suggested Citation

  • M. Fürst & D. Rautenbach, 2019. "On some hard and some tractable cases of the maximum acyclic matching problem," Annals of Operations Research, Springer, vol. 279(1), pages 291-300, August.
    • Handle: RePEc:spr:annopr:v:279:y:2019:i:1:d:10.1007_s10479-019-03311-1
    DOI: 10.1007/s10479-019-03311-1
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    Cited by:

    1. Péter Madarasi, 2021. "Matchings under distance constraints I," Annals of Operations Research, Springer, vol. 305(1), pages 137-161, October.

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