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In graph theory, an exact coloring is a (proper) vertex coloring in which every pair of colors appears on exactly one pair of adjacent vertices. That is, it is a partition of the vertices of the graph into disjoint independent sets such that, for each pair of distinct independent sets in the partition, there is exactly one edge with endpoints in each set.〔.〕〔.〕 ==Complete graphs, detachments, and Euler tours== Every ''n''-vertex complete graph ''K''''n'' has an exact coloring with ''n'' colors, obtained by giving each vertex a distinct color. Every graph with an ''n''-color exact coloring may be obtained as a ''detachment'' of a complete graph, a graph obtained from the complete graph by splitting each vertex into an independent set and reconnecting each edge incident to the vertex to exactly one of the members of the corresponding independent set.〔〔 When ''k'' is an odd number, A path or cycle with edges has an exact coloring, obtained by forming an exact coloring of the complete graph ''K''''k'' and then finding an Euler tour of this complete graph. For instance, a path with three edges has a complete 3-coloring.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Exact coloring」の詳細全文を読む スポンサード リンク
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