Cyclability: различия между версиями
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'''Cyclability''' --- | '''Cyclability''' — ''[[цикличность]]''. | ||
A subset <math>\,S</math> of [[vertex|vertices]] of a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> is called '''cyclable''' in | |||
<math>\,G</math> if there is in <math>\,G</math> some cycle containing all the vertices of <math>\,S</math>. | |||
It is known that if <math>\,G</math> is a [[k-Connected graph|<math>\,3</math>-connected graph]] of order <math>\,n</math> and if <math>\,S</math> | |||
is a subset of vertices such that the degree sum of any four independent vertices of <math>\,S</math> is at least <math>\,n + 2\alpha (S,G) - 2</math>, then <math>\,S</math> is cyclable. Here <math>\alpha (S,G)</math> is the number of vertices of a maximum independent set of <math>\,G[S]</math>. | |||
==See also== | ==See also== | ||
*''Pancyclable graph''. | |||
* ''[[Pancyclic graph|Pancyclable graph]]''. | |||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 15:57, 14 декабря 2021
Cyclability — цикличность.
A subset [math]\displaystyle{ \,S }[/math] of vertices of a graph [math]\displaystyle{ \,G }[/math] is called cyclable in [math]\displaystyle{ \,G }[/math] if there is in [math]\displaystyle{ \,G }[/math] some cycle containing all the vertices of [math]\displaystyle{ \,S }[/math]. It is known that if [math]\displaystyle{ \,G }[/math] is a [math]\displaystyle{ \,3 }[/math]-connected graph of order [math]\displaystyle{ \,n }[/math] and if [math]\displaystyle{ \,S }[/math] is a subset of vertices such that the degree sum of any four independent vertices of [math]\displaystyle{ \,S }[/math] is at least [math]\displaystyle{ \,n + 2\alpha (S,G) - 2 }[/math], then [math]\displaystyle{ \,S }[/math] is cyclable. Here [math]\displaystyle{ \alpha (S,G) }[/math] is the number of vertices of a maximum independent set of [math]\displaystyle{ \,G[S] }[/math].
See also
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.