K-Cyclic chromatic number: различия между версиями

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'''<math>k</math>-Cyclic chromatic number''' --- <math>k</math>-циклическое хроматическое
'''<math>k</math>-Cyclic chromatic number''' — ''[[k-циклическое хроматическое число|<math>\,k</math>-циклическое хроматическое число]]''.  
число.  


The '''<math>k</math>-cyclic chromatic number''' <math>\chi_{k}(G)</math> of a plane graph is the smallest number of colours in a vertex colouring of <math>G</math> such that no face of
The '''<math>\,k</math>-cyclic chromatic number''' <math>\,\chi_{k}(G)</math> of a [[plane graph]] is the smallest number of colours in a [[vertex]] [[Coloring, colouring|colouring]] of <math>\,G</math> such that no face of size at most <math>\,k</math> has two boundary vertices of the same colour. It is easy to see that the Four Colour Theorem may be stated in the form:
size at most <math>k</math> has two boundary vertices of the same colour. It is
easy to see that the Four Colour Theorem may be stated in the form:


<math>\chi_{3}(G) \leq 4</math>
<math>\,\chi_{3}(G) \leq 4</math>


for every plane graph <math>G</math>.
for every plane graph <math>\,G</math>.


The number <math>\chi_{k}(G)</math> was introduced explicitly by Ore and Plummer
The number <math>\,\chi_{k}(G)</math> was introduced explicitly by Ore and Plummer (1969).
(1969).
 
==Литература==
*Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.

Текущая версия от 15:13, 4 декабря 2023

[math]\displaystyle{ k }[/math]-Cyclic chromatic number[math]\displaystyle{ \,k }[/math]-циклическое хроматическое число.

The [math]\displaystyle{ \,k }[/math]-cyclic chromatic number [math]\displaystyle{ \,\chi_{k}(G) }[/math] of a plane graph is the smallest number of colours in a vertex colouring of [math]\displaystyle{ \,G }[/math] such that no face of size at most [math]\displaystyle{ \,k }[/math] has two boundary vertices of the same colour. It is easy to see that the Four Colour Theorem may be stated in the form:

[math]\displaystyle{ \,\chi_{3}(G) \leq 4 }[/math]

for every plane graph [math]\displaystyle{ \,G }[/math].

The number [math]\displaystyle{ \,\chi_{k}(G) }[/math] was introduced explicitly by Ore and Plummer (1969).

Литература

  • Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.