Arbitrarily vertex decomposable graph — различия между версиями

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'''Arbitrarily vertex decomposable graph''' --- произвольно
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'''Arbitrarily vertex decomposable graph''' — ''[[произвольно вершинно разложимый граф]].''
вершинно разложимый граф.  
 
  
A graph <math>G</math> of order <math>n</math> is said to be '''arbitrarily vertex
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A [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> of order <math>\,n</math> is said to be '''arbitrarily vertex decomposable''', if for each sequence <math>(n_{1}, \ldots, n_{k})</math> of positive integers such that <math>n_{1} + \ldots + n_{k} = n</math> there exists
decomposable''', if for each sequence <math>(n_{1}, \ldots, n_{k})</math> of
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a partition <math>(V_{1}, \ldots, V_{k})</math> of the [[vertex]] set of <math>\,G</math> such
positive integers such that <math>n_{1} + \ldots + n_{k} = n</math> there exists
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that, for each <math>i \in \{1, \ldots, k\}</math>, <math>V_{i}</math> induces a [[connected graph|connected]] [[subgraph]] of <math>\,G</math> on <math>\,n_{i}</math> vertices.
a partition <math>(V_{1}, \ldots, V_{k})</math> of the vertex set of <math>G</math> such
 
that, for each <math>i \in \{1, \ldots, k\}</math>, <math>V_{i}</math> induces a connected
 
subgraph of <math>G</math> on <math>n_{i}</math> vertices.
 
  
 
==See also==
 
==See also==
  
*''Admissible sequence''.
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* ''[[Admissible sequence]]''.

Текущая версия на 11:24, 5 декабря 2011

Arbitrarily vertex decomposable graphпроизвольно вершинно разложимый граф.

A graph \,G of order \,n is said to be arbitrarily vertex decomposable, if for each sequence (n_{1}, \ldots, n_{k}) of positive integers such that n_{1} + \ldots + n_{k} = n there exists a partition (V_{1}, \ldots, V_{k}) of the vertex set of \,G such that, for each i \in \{1, \ldots, k\}, V_{i} induces a connected subgraph of \,G on \,n_{i} vertices.

See also