Transitive tournament

Transitive tournament --- транзитивный турнир.

A tournament [math]\displaystyle{ T }[/math] such that [math]\displaystyle{ (x,y) \in E(T) }[/math] and [math]\displaystyle{ (y,z) \in E(T) }[/math] imply [math]\displaystyle{ (x,y) \in E(T) }[/math] is called transitive. The vertices of a transitive tournament have an ordering [math]\displaystyle{ (x_{1}, \ldots, x_{n}) }[/math] such that [math]\displaystyle{ (x_{i},x_{j}) \in E(G) \leftrightarrow i \lt j }[/math].

A tournament [math]\displaystyle{ T }[/math] is quasi-transitive, if [math]\displaystyle{ v_{k} \Rightarrow v_{k+1} }[/math] and [math]\displaystyle{ v_{j} \Rightarrow v_{i} }[/math], whenever [math]\displaystyle{ 1 \leq k \leq n-1 }[/math] and [math]\displaystyle{ 1 \leq i \lt j-1 \leq n-1 }[/math]. ([math]\displaystyle{ u \Rightarrow v }[/math] means that [math]\displaystyle{ (u,v) }[/math] is an arc in [math]\displaystyle{ T }[/math].)