Achromatic number: различия между версиями
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Glk (обсуждение | вклад) (Создана новая страница размером '''Achromatic number''' --- ахроматическое число. The '''achromatic number''' <math>\psi(G)</math> of <math>G</mat...) |
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'''Achromatic number''' | '''Achromatic number''' — ''[[ахроматическое число]].'' | ||
The '''achromatic number''' <math>\psi(G)</math> of <math>G</math> is the maximum number of sets in a | The '''achromatic number''' <math>\,\psi(G)</math> of <math>\,G</math> is the maximum number of sets in a partition of <math>\,V</math> into ''independent'' subsets <math>V_{1}, V_{2}, \ldots, | ||
partition of <math>V</math> into ''independent'' subsets <math>V_{1}, V_{2}, \ldots, | |||
V_{k}</math> such that | V_{k}</math> such that | ||
(1) each <math>V_{i}</math> is an independent set of vertices, and | (1) each <math>\,V_{i}</math> is an independent set of vertices, and | ||
(2) for <math>i \neq j</math>, there exists <math>v_{i} \in V_{i}</math> and <math>v_{j} \in | (2) for <math>i \neq j</math>, there exists <math>v_{i} \in V_{i}</math> and <math>v_{j} \in | ||
V_{j}</math> such that <math>v_{i}v_{j} \in E(G)</math>. | V_{j}</math> such that <math>v_{i}v_{j} \in E(G)</math>. | ||
Версия от 16:26, 1 ноября 2011
Achromatic number — ахроматическое число.
The achromatic number [math]\displaystyle{ \,\psi(G) }[/math] of [math]\displaystyle{ \,G }[/math] is the maximum number of sets in a partition of [math]\displaystyle{ \,V }[/math] into independent subsets [math]\displaystyle{ V_{1}, V_{2}, \ldots, V_{k} }[/math] such that
(1) each [math]\displaystyle{ \,V_{i} }[/math] is an independent set of vertices, and
(2) for [math]\displaystyle{ i \neq j }[/math], there exists [math]\displaystyle{ v_{i} \in V_{i} }[/math] and [math]\displaystyle{ v_{j} \in V_{j} }[/math] such that [math]\displaystyle{ v_{i}v_{j} \in E(G) }[/math].