K-Choosable graph: различия между версиями
Перейти к навигации
Перейти к поиску
Glk (обсуждение | вклад) (Новая страница: «'''<math>k</math>-Choosable graph''' --- <math>k</math>-выбираемый граф. '''1.''' A graph <math>G</math> is '''<math>k</math>-choosable''' if its ''…») |
KEV (обсуждение | вклад) Нет описания правки |
||
| Строка 1: | Строка 1: | ||
'''<math>k</math>-Choosable graph''' - | '''<math>\,k</math>-Choosable graph''' — [[k-выбираемый граф|<math>\,k</math>-выбираемый граф]]. | ||
'''1.''' A graph <math>G</math> is '''<math>k</math>-choosable''' if its ''list chromatic number'' | '''1.''' A [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> is '''<math>\,k</math>-choosable''' if its ''[[list chromatic number]]'' | ||
satisfies the inequality <math>\chi_{\ell} (G) \leq k</math>. | satisfies the inequality <math>\chi_{\ell} (G) \leq k</math>. | ||
'''2.''' A graph <math>G</math> is '''<math>k</math>-choosable''' if, whenever each vertex <math>v</math> is given a ''list'' (set) <math>L(v)</math> of <math>k</math> colours, <math>G</math> has a '' proper colouring'' in which each vertex receives a colour from its own list. | '''2.''' A graph <math>\,G</math> is '''<math>\,k</math>-choosable''' if, whenever each [[vertex]] <math>\,v</math> is given a ''list'' (set) <math>\,L(v)</math> of <math>\,k</math> colours, <math>\,G</math> has a ''[[proper coloring|proper colouring]]'' in which each vertex receives a colour from its own list. | ||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 17:55, 28 марта 2013
[math]\displaystyle{ \,k }[/math]-Choosable graph — [math]\displaystyle{ \,k }[/math]-выбираемый граф.
1. A graph [math]\displaystyle{ \,G }[/math] is [math]\displaystyle{ \,k }[/math]-choosable if its list chromatic number satisfies the inequality [math]\displaystyle{ \chi_{\ell} (G) \leq k }[/math].
2. A graph [math]\displaystyle{ \,G }[/math] is [math]\displaystyle{ \,k }[/math]-choosable if, whenever each vertex [math]\displaystyle{ \,v }[/math] is given a list (set) [math]\displaystyle{ \,L(v) }[/math] of [math]\displaystyle{ \,k }[/math] colours, [math]\displaystyle{ \,G }[/math] has a proper colouring in which each vertex receives a colour from its own list.
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.