Subgraph derivation

Subgraph derivation --- вывод подграфа (подграфовый вывод).

A graph [math]\displaystyle{ H' }[/math] is directly subgraph derivable from a graph [math]\displaystyle{ G }[/math], denoted by [math]\displaystyle{ G \mapsto H' }[/math], if there is a graph [math]\displaystyle{ H }[/math], such that [math]\displaystyle{ G \Longrightarrow H }[/math] and [math]\displaystyle{ H' }[/math] is a subgraph of [math]\displaystyle{ H }[/math].

We say [math]\displaystyle{ G \stackrel{\ast}{\mapsto} H }[/math] is a subgraph derivation, where [math]\displaystyle{ \stackrel{\ast}{\mapsto} }[/math] is the transitive and reflexive closure of [math]\displaystyle{ \mapsto }[/math]; in that case, we also say that [math]\displaystyle{ H }[/math] is subgraph derivable from [math]\displaystyle{ G }[/math].