A counterexample to a conjecture of Schwartz
Résumé
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 paper, and so Schwartz’ conjecture is false. Our proof is non-constructive and uses the probabilistic method.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
|---|