H-forming set

[math]\displaystyle{ H }[/math]-forming set --- [math]\displaystyle{ H }[/math]-формирующее множество.

For graphs [math]\displaystyle{ G }[/math] and [math]\displaystyle{ H }[/math], a set [math]\displaystyle{ S \subseteq V(G) }[/math] is an [math]\displaystyle{ H }[/math]-forming set of [math]\displaystyle{ G }[/math] if for every [math]\displaystyle{ v \in V(G) - S }[/math], there exists a subset [math]\displaystyle{ R \subseteq S }[/math], where [math]\displaystyle{ |R| = |V(H)| - 1 }[/math], such that the subgraph induced by [math]\displaystyle{ R \cup \{v\} }[/math] contains [math]\displaystyle{ H }[/math] as a subgraph (not necessarily induced). The minimum cardinality of an [math]\displaystyle{ H }[/math]-forming set of [math]\displaystyle{ G }[/math] is the [math]\displaystyle{ H }[/math]-forming number [math]\displaystyle{ \gamma_{\{H\}}(G) }[/math]. The [math]\displaystyle{ H }[/math]-forming number of [math]\displaystyle{ G }[/math] is a generalization of the domination number [math]\displaystyle{ \gamma(G) }[/math].