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

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

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

The number <math>\,\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.