Social Choice and Welfare

, Volume 40, Issue 3, pp 739–743 | Cite as

A counterexample to a conjecture of Schwartz

  • Felix Brandt
  • Maria Chudnovsky
  • Ilhee Kim
  • Gaku Liu
  • Sergey Norin
  • Alex Scott
  • Paul Seymour
  • Stephan Thomassé
Original Paper

Abstract

In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A, B of its vertex set, such that every transitive subset of A is in the out-neighbour set of some vertex in B, and vice versa. But in fact there is such a tournament, as we show in this article, and so Schwartz’ conjecture is false. Our proof is non-constructive and uses the probabilistic method.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Felix Brandt
    • 1
  • Maria Chudnovsky
    • 2
  • Ilhee Kim
    • 3
  • Gaku Liu
    • 3
  • Sergey Norin
    • 4
  • Alex Scott
    • 5
  • Paul Seymour
    • 3
  • Stephan Thomassé
    • 6
  1. 1.Technische Universität MünchenMunichGermany
  2. 2.Columbia UniversityNew YorkUSA
  3. 3.Princeton UniversityPrincetonUSA
  4. 4.McGill UniversityMontrealCanada
  5. 5.University of OxfordOxfordUK
  6. 6.Université Montpelier 2MontpelierFrance

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