Phylogeny digraph

Phylogeny digraph --- филогенный орграф.

Given a graph [math]\displaystyle{ G = (V,E) }[/math], the acyclic digraph [math]\displaystyle{ D }[/math] is a phylogeny digraph for [math]\displaystyle{ G }[/math] if [math]\displaystyle{ G }[/math] is an induced subgraph of a phylogeny graph [math]\displaystyle{ P(D) }[/math] and [math]\displaystyle{ D }[/math] has no arcs from vertices outside of [math]\displaystyle{ G }[/math] to vertices in [math]\displaystyle{ G }[/math].

The phylogeny number [math]\displaystyle{ p(G) }[/math] is defined to be the smallest [math]\displaystyle{ r }[/math] such that [math]\displaystyle{ G }[/math] has a phylogeny digraph [math]\displaystyle{ D }[/math] with [math]\displaystyle{ |V(D) - V(G)| = r }[/math].