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The matching extension problem in general graphs is co-NP-complete

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Abstract

A simple connected graph G with 2n vertices is said to be k-extendable for an integer k with \(0<k<n\) if G contains a perfect matching and every matching of cardinality k in G is a subset of some perfect matching. Lakhal and Litzler (Inf Process Lett 65(1):11–16, 1998) discovered a polynomial algorithm that decides whether a bipartite graph is k-extendable. For general graphs, however, it has been an open problem whether there exists a polynomial algorithm. The new result presented in this paper is that the extendability problem is co-NP-complete.

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Authors and Affiliations

  1. School of Business and Economics, Humboldt-Universität zu Berlin, Spandauer Straße 1, 10178, Berlin, Germany

    Jan Hackfeld

  2. Lehrstuhl II für Mathematik, RWTH Aachen University, 52056, Aachen, Germany

    Arie M. C. A. Koster

Authors
  1. Jan Hackfeld
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  2. Arie M. C. A. Koster
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Correspondence to Jan Hackfeld.

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Hackfeld, J., Koster, A.M.C.A. The matching extension problem in general graphs is co-NP-complete. J Comb Optim 35, 853–859 (2018). https://doi.org/10.1007/s10878-017-0226-x

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  • DOI: https://doi.org/10.1007/s10878-017-0226-x

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