Tournament

Tournament --- турнир.

An oriented complete graph, i.e. a (simple) digraph [math]\displaystyle{ T }[/math] without loops in which exactly one of [math]\displaystyle{ (x,y) }[/math] or [math]\displaystyle{ (y,x) }[/math] is an arc for every pair [math]\displaystyle{ x \neq y }[/math], [math]\displaystyle{ x,y \in T }[/math]. The vertex [math]\displaystyle{ v }[/math] of a tournament [math]\displaystyle{ T }[/math] has a positive (negative) valence [math]\displaystyle{ k }[/math], if there are [math]\displaystyle{ k }[/math] arcs from (into) [math]\displaystyle{ v }[/math]. A tournament [math]\displaystyle{ T }[/math] is regular of degree [math]\displaystyle{ t }[/math], if the positive valence of each of its vertices is [math]\displaystyle{ t }[/math]. A tournament is doubly regular with a subdegree [math]\displaystyle{ t }[/math], if all pairs of vertices jointly dominate precisely [math]\displaystyle{ t }[/math] vertices. A tournament [math]\displaystyle{ T }[/math] is called almost regular, when [math]\displaystyle{ \Delta = \delta }[/math].

See also

• Transitive tournament,
• Quasi-transitive tournament.