Arbitrarily vertex decomposable graph — различия между версиями
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| − | '''Arbitrarily vertex decomposable graph''' | + | '''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 | + | 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 | + | 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 | + | 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''. | + | * ''[[Admissible sequence]]''. |
Текущая версия на 11:24, 5 декабря 2011
Arbitrarily vertex decomposable graph — произвольно вершинно разложимый граф.
A graph 
of order 
is said to be arbitrarily vertex decomposable, if for each sequence 
of positive integers such that 
there exists
a partition 
of the vertex set of such
that, for each 
, 
induces a connected subgraph of on 
vertices.
