A counterexample to a conjecture of Schwartz

Ilhee Kim (김일희)

Princeton University, Princeton, NJ, USA

Princeton University, Princeton, NJ, USA

2012/01/11 Wed 4PM-5PM

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 and so Schwartz’ conjecture is false. Our proof is non-constructive and uses the probabilistic method.

This is joint work with Felix Brandt, Gaku Liu, Maria Chudnovsky, Sergey Norin, Alex Scott, Paul Seymour, and Stephan Thomassé.

This is joint work with Felix Brandt, Gaku Liu, Maria Chudnovsky, Sergey Norin, Alex Scott, Paul Seymour, and Stephan Thomassé.

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