Critical tournament

Critical tournament — критический турнир.

Given a tournament [math]\displaystyle{ \,T = (V,A) }[/math], a subset [math]\displaystyle{ \,X }[/math] of [math]\displaystyle{ \,V }[/math] is an interval of [math]\displaystyle{ \,T }[/math] provided that for every [math]\displaystyle{ \,a, b \in X }[/math] and [math]\displaystyle{ \,x \in V - X }[/math], [math]\displaystyle{ \,(a,x) \in A }[/math] if and only if [math]\displaystyle{ \,(b,x) \in A }[/math]. For example, [math]\displaystyle{ \,\emptyset }[/math], [math]\displaystyle{ \,\{x\} \; (x \in V) }[/math] and [math]\displaystyle{ \,V }[/math] are intervals, called trivial intervals. A tournament all intervals of which are trivial is called indecomposable; otherwise, it is decomposable. An indecomposable tournament [math]\displaystyle{ \,T = (V,A) }[/math] is then said to be critical if for each [math]\displaystyle{ \,x \in V }[/math], [math]\displaystyle{ \,T(V - \{x\}) }[/math] is decomposable and if there are [math]\displaystyle{ \,x \neq y \in V }[/math] such that [math]\displaystyle{ \,T(V - \{x,y\}) }[/math] is indecomposable.

Литература

• Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.