Domination graph (of a tournament)

Domination graph (of a tournament) --- граф доминирования.

The vertices [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] dominate a tournament [math]\displaystyle{ T }[/math] if for all vertices [math]\displaystyle{ z \neq x, y }[/math], either [math]\displaystyle{ x }[/math] beats [math]\displaystyle{ z }[/math] or [math]\displaystyle{ y }[/math] beats [math]\displaystyle{ z }[/math]. Let dom([math]\displaystyle{ T }[/math]) be a graph on the vertices of [math]\displaystyle{ T }[/math] with edges between pairs of vertices that dominate [math]\displaystyle{ T }[/math]. This graph is called a domination graph. It is known that dom([math]\displaystyle{ T }[/math]) is either an odd cycle with possible pendant vertices or a forest of caterpillars. Also a domination graph is the complement of the competition graph of the tournament.