Compact closed class of graphs — различия между версиями

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'''Compact closed class of graphs''' --- компактно замкнутый класс графов.  
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'''Compact closed class of graphs''' — ''[[компактно замкнутый класс графов]].''
  
A class <math>{\mathcal C}</math> of graphs is said to be '''compact closed''' if,
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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
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contained in a finite induced subgraph of <math>G</math> which belongs to the
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==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
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of <math>G</math> is contained in a finite induced subgraph of <math>G</math> which belongs
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* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.
to <math>{\mathcal C}</math>.
 

Текущая версия на 14:23, 1 октября 2014

Compact closed class of graphsкомпактно замкнутый класс графов.

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

Литература

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