Strongly perfect graph

Strongly perfect graph --- строго совершенный граф.

[math]\displaystyle{ G }[/math] is a strongly perfect graph if each induced subgraph [math]\displaystyle{ H }[/math] of [math]\displaystyle{ G }[/math] has a stable set meeting all maximal cliques in [math]\displaystyle{ H }[/math]: for all [math]\displaystyle{ V' \subseteq V }[/math] there is [math]\displaystyle{ S \subseteq V' }[/math] stable in [math]\displaystyle{ G[V'] }[/math] such that for all maximal cliques [math]\displaystyle{ C }[/math] in [math]\displaystyle{ G[V'] }[/math] [math]\displaystyle{ |S \cap C| = 1 }[/math]. The class of strongly perfect graph is the proper subclass of perfect graphs.

[math]\displaystyle{ G }[/math] is very strongly perfect, if for each induced subgraph [math]\displaystyle{ H }[/math] of [math]\displaystyle{ G }[/math] each vertex of [math]\displaystyle{ H }[/math] belongs to a stable set of [math]\displaystyle{ H }[/math] meeting all maximal cliques of [math]\displaystyle{ H }[/math]. Very strongly perfect graphs are also strongly perfect.