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Algorithms for enumerating all perfect, maximum and maximal matchings in bipartite graphs

  • Takeaki Uno
Session 3A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1350)

Abstract

For a bipartite graph G = (V, E), (1) perfect, (2) maximum and (3) maximal matchings are matchings (1) such that all vertices are incident to some matching edges, (2) whose cardinalities are maximum among all matchings, (3) which are contained in no other matching. In this paper, we present three algorithms for enumerating these three types of matchings. Their time complexities are O(|V |) per a matching.

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References

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    K. Fukuda and T. Matsui, “Finding All the Perfect Matthings in Bipartite Graphs,” Appl. Math. Lett. 7 1 (1994) 15–18Google Scholar
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    J. E. Hopcroft and R. M. Karp, “An n 5/2 algorithm for maximum matching in bipartite graphs,” SIAM J. on Comp., Vol. 2: 225–231, 1973.Google Scholar
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    R. E. Tarjan, “Depth-First Search and Linear Graph Algorithm,” SIAM J. Comp. 1, 146–169, 1972.Google Scholar
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    S.Tsukiyama, M.Ide, H.Ariyoshi and I.Shirakawa, “A New Algorithm for Generating All the Maximum Independent Sets,” SIAM J. Comp.,Vol.6, No.3: 505–517,1977.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Takeaki Uno
    • 1
  1. 1.Department of Systems ScienceTokyo Institute of TechnologyMeguro-ku, TokyoJapan

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