Compact closed class of graphs: различия между версиями
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'''Compact closed class of graphs''' | '''Compact closed class of graphs''' — ''[[компактно замкнутый класс графов]].'' | ||
A class <math>{\mathcal C}</math> of graphs is said to be '''compact closed''' if, | A class <math>\,{\mathcal C}</math> of [[graph, undirected graph, nonoriented graph|graphs]] is said to be '''compact closed''' if, whenever a graph <math>\,G</math> is such that each of its [[finite graph|finite]] [[subgraph|subgraphs]] is contained in a finite [[induced (with vertices) subgraph|induced subgraph]] of <math>\,G</math> which belongs to the class <math>\,{\mathcal C}</math>, the graph <math>\,G</math> itself belongs to <math>\,{\mathcal C}</math>. We will say that a class <math>\,{\mathcal C}</math> of graphs is '''dually compact closed''' if, for every infinite <math>\,G \in {\mathcal C}</math>, each finite subgraph of <math>\,G</math> is contained in a finite induced subgraph of <math>\,G</math> which belongs to <math>\,{\mathcal C}</math>. | ||
whenever a graph <math>G</math> is such that each of its finite subgraphs is | |||
contained in a finite induced subgraph of <math>G</math> which belongs to the | ==Литература== | ||
class <math>{\mathcal C}</math>, the graph <math>G</math> itself belongs to <math>{\mathcal C}</math>. We will say that a class <math>{\mathcal C}</math> of graphs is '''dually compact closed''' if, for every infinite <math>G \in {\mathcal C}</math>, each finite subgraph | |||
of <math>G</math> is contained in a finite induced subgraph of <math>G</math> which belongs | * Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | ||
to <math>{\mathcal C}</math>. | |||
Текущая версия от 10:46, 24 октября 2018
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.