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Bisection width of a graph: различия между версиями
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'''Bisection width of a graph''' | '''Bisection width of a graph''' — ''[[ширина бисекции графа]].'' | ||
The '''bisection width''' <math>bw(G)</math> '''of a graph''' <math>G</math> is the minimal number of edges | The '''bisection width''' <math>\,bw(G)</math> '''of a graph''' <math>\,G</math> is the minimal number of [[edge|edges]] | ||
between vertex sets <math>A</math> and <math>\bar{A}</math> of almost equal sizes, i.e. <math>A | between [[vertex]] sets <math>\,A</math> and <math>\bar{A}</math> of almost equal sizes, i.e. <math>A | ||
\cup \bar{A} = V(G)</math> and <math>||A| - |\bar{A}|| \leq 1</math>. If <math>A \subseteq | \cup \bar{A} = V(G)</math> and <math>||A| - |\bar{A}|| \leq 1</math>. If <math>A \subseteq | ||
V(G)</math>, then <math>E(A,\bar{A})</math> denotes the set of edges of <math>G</math> having one | V(G)</math>, then <math>E(A,\bar{A})</math> denotes the set of edges of <math>\,G</math> having one | ||
end in <math>A</math> and another end in <math>V(G) \setminus A = \bar{A}</math>. The '''isoperimetric number''' <math>i(G)</math> of a graph <math>G</math> equals the minimum | end in <math>\,A</math> and another end in <math>V(G) \setminus A = \bar{A}</math>. The '''[[isoperimetric number]]''' <math>\,i(G)</math> of a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> equals the minimum | ||
of the ratio <math>|E(A,\bar{A}|/|A|</math> for all <math>A \subseteq V(G)</math> such that | of the ratio <math>|E(A,\bar{A}|/|A|</math> for all <math>A \subseteq V(G)</math> such that | ||
<math>2|A| \leq |V(G)| = n</math>. | <math>2|A| \leq |V(G)| = n</math>. | ||
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characteristics: | characteristics: | ||
<math>i(G) \leq \frac{2}{n}bw(G).</math> | :::::<math>i(G) \leq \frac{2}{n}bw(G).</math> | ||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
