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Brooks’ theorem : ウィキペディア英語版
Brooks' theorem

In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected graph in which every vertex has at most Δ neighbors, the vertices can be colored with only Δ colors, except for two cases, complete graphs and cycle graphs of odd length, which require Δ + 1 colors.
The theorem is named after R. Leonard Brooks, who published a proof of it in 1941. A coloring with the number of colors described by Brooks' theorem is sometimes called a ''Brooks coloring'' or a Δ-''coloring''.
==Formal statement==
For any connected undirected graph ''G'' with maximum degree Δ,
the chromatic number of ''G'' is at most Δ unless ''G'' is a complete graph or an odd cycle, in which case the chromatic number is Δ + 1.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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