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|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.|
|Electronic Publication Date:||17-Jan-2012|
|Citation:||Brandt, Felix, Chudnovsky, Maria, Kim, Ilhee, Liu, Gaku, Norin, Sergey, Scott, Alex, Seymour, Paul, Thomassé, Stephan. (2013). A counterexample to a conjecture of Schwartz. Social Choice and Welfare, 40 (3), 739 - 743. doi:10.1007/s00355-011-0638-y|
|Pages:||739 - 743|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Social Choice and Welfare|
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