Transitive reduction of a digraph

Transitive reduction of a digraph --- транзитивная редукция орграфа.

A transitive reduction [math]\displaystyle{ TR }[/math] of a digraph [math]\displaystyle{ G = (V,A) }[/math] is a digraph [math]\displaystyle{ G^{-} = (V,A^{-}) }[/math] having the minimum number of arcs and the same transitive closure of [math]\displaystyle{ G }[/math]. It is known that, for any dag [math]\displaystyle{ G }[/math], the transitive reduction [math]\displaystyle{ G^{-} }[/math] is unique and is a subgraph (partial graph) of [math]\displaystyle{ G }[/math].