Indecomposable tournaments and their indecomposable subtournaments with six vertices

Given a tournament T = (V, A), a subset X of V is an interval of T provided that, for any a, b is an element of X and x is an element of V - X, (a, x) is an element of A if and only if (b, x) is an element of A. For example, empty set, {x}(x is an element of V) and V are intervals of T, called trivial intervals. A tournament, all the intervals of which are trivial, is indecomposable; otherwise, it is decomposable. We say that a tournament T' embeds in a tournament T when T' is isomorphic to a subtournament of T. In this article, we classify the indecomposable tournaments according to the indecomposable tournaments with six vertices embedding in T. (C) 2015 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.