Tournois sans intervalle acyclique

An interval X of a tournament T is a vertex subset of T such that any vertex not in X either dominates or is dominated by all of the vertices in X. We caracterize the tournaments such that the only non empty acyclic intervals are the singletons and which are critical for that property, that is whenever a vertex is removed at least one acyclic interval with more than 2 vertices is created. These tournaments are exactly those which are the composition of any tournament with circulant tournaments. That work on acyclic intervals was motivated by the study of tournaments for which no median order forced itself naturally. To cite this article: J.-F. Culus, B. Jouve, C. R. Acad. Sci. Paris, Ser. I 341 (2005).