Circular clique number: различия между версиями

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'''Circular clique number''' --- цикловое кликовое число.  
'''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 numberцикловое 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.