Circular clique number: различия между версиями
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'''Circular clique number''' | '''Circular clique number''' — ''[[цикловое кликовое число]].'' | ||
The '''circular clique number''' of a graph <math>G</math>, denoted by <math>\omega_{c}(G)</math>, | The '''circular clique number''' of a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math>, denoted by <math>\,\omega_{c}(G)</math>, | ||
is defined as the maximum quotient <math>k/d</math> such that the graph <math>G_{d}^{k}</math> | is defined as the maximum quotient <math>\,k/d</math> such that the graph <math>\,G_{d}^{k}</math> | ||
(<math>k \geq 2d</math>) | (<math>k \geq 2d</math>) | ||
admits a homomorphism to <math>G</math>. | admits a homomorphism to <math>\,G</math>. | ||
The graph <math>G_{d}^{k}</math> is defined as follows: | The graph <math>G_{d}^{k}</math> is defined as follows: | ||
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<math>E(G_{d}^{k}) = \{v_{i},v_{j} : d \leq |j - i| \leq k-d \bmod k\}.</math> | <math>E(G_{d}^{k}) = \{v_{i},v_{j} : d \leq |j - i| \leq k-d \bmod k\}.</math> | ||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 18:15, 11 июня 2013
Circular clique number — цикловое кликовое число.
The circular clique number of a graph [math]\displaystyle{ \,G }[/math], denoted by [math]\displaystyle{ \,\omega_{c}(G) }[/math], is defined as the maximum quotient [math]\displaystyle{ \,k/d }[/math] such that the graph [math]\displaystyle{ \,G_{d}^{k} }[/math] ([math]\displaystyle{ k \geq 2d }[/math]) admits a homomorphism to [math]\displaystyle{ \,G }[/math].
The graph [math]\displaystyle{ G_{d}^{k} }[/math] is defined as follows:
[math]\displaystyle{ V(G_{d}^{k}) = \{v_{0}, v_{1}, \ldots, v_{k-1}\} }[/math],
[math]\displaystyle{ E(G_{d}^{k}) = \{v_{i},v_{j} : d \leq |j - i| \leq k-d \bmod k\}. }[/math]
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.