Transformation from arbitrary matchings to stable matchings

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15 Citations (Scopus)


D. E. Knuth (1976, "Mariages stables," Presses Univ. Montréal, Montreal) conjectured that any matching can be transformed to some stable matching by a sequence of b-interchanges. Given a matching M and a blocking pair (m, w) for M, a b-interchange for M by (m, w) is defined as a transformation from M to a matching obtained by replacing two pairs (m, pM (m)) and (pM (w), w) in M with (m, w) and (pM (w), pM (m)). In this paper, we give a counter-example in which some matching cannot be transformed to any stable matching by b-interchanges. However, any matching can be transformed to some stable matching by using b-interchanges and identifying special cycling. We also give an algorithm to find either such cycling or a stable matching.

Original languageEnglish
Pages (from-to)310-323
Number of pages14
JournalJournal of Combinatorial Theory, Series A
Issue number2
Publication statusPublished - 1993 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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