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

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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 \(P_4\)-free graphs and \(2P_3\)-free graphs, and we characterize the graphs for which every maximum matching is acyclic.

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Authors and Affiliations

  1. Institute of Optimization and Operations Research, Ulm University, Ulm, Germany

    M. Fürst & D. Rautenbach

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  1. M. Fürst
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  2. D. Rautenbach
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Correspondence to D. Rautenbach.

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Fürst, M., Rautenbach, D. On some hard and some tractable cases of the maximum acyclic matching problem. Ann Oper Res 279, 291–300 (2019). https://doi.org/10.1007/s10479-019-03311-1

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