Compact closed class of graphs

Compact closed class of graphs — компактно замкнутый класс графов.

A class [math]\displaystyle{ \,{\mathcal C} }[/math] of graphs is said to be compact closed if, whenever a graph [math]\displaystyle{ \,G }[/math] is such that each of its finite subgraphs is contained in a finite induced subgraph of [math]\displaystyle{ \,G }[/math] which belongs to the class [math]\displaystyle{ \,{\mathcal C} }[/math], the graph [math]\displaystyle{ \,G }[/math] itself belongs to [math]\displaystyle{ \,{\mathcal C} }[/math]. We will say that a class [math]\displaystyle{ \,{\mathcal C} }[/math] of graphs is dually compact closed if, for every infinite [math]\displaystyle{ \,G \in {\mathcal C} }[/math], each finite subgraph of [math]\displaystyle{ \,G }[/math] is contained in a finite induced subgraph of [math]\displaystyle{ \,G }[/math] which belongs to [math]\displaystyle{ \,{\mathcal C} }[/math].

Литература

• Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.