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In mathematics, list edge-coloring is a type of graph coloring that combines list coloring and edge coloring. An instance of a list edge-coloring problem consists of a graph together with a list of allowed colors for each edge. A list edge-coloring is a choice of a color for each edge, from its list of allowed colors; a coloring is proper if no two adjacent edges receive the same color. A graph ''G'' is ''k''-edge-choosable if every instance of list edge-coloring that has ''G'' as its underlying graph and that provides at least ''k'' allowed colors for each edge of ''G'' has a proper coloring. The edge choosability, or ''list edge colorability'', ''list edge chromatic number'', or ''list chromatic index'', ch′(''G'') of graph ''G'' is the least number ''k'' such that ''G'' is ''k''-edge-choosable. ==Properties== Some properties of ch′(''G''): # ch′(''G'') < 2 χ′(''G''). # ch′(K''n'',''n'') = ''n''. This is the Dinitz conjecture, proven by . # ch′(''G'') < (1 + o(1))χ′(''G''), i.e. the list chromatic index and the chromatic index agree asymptotically . Here χ′(''G'') is the chromatic index of ''G''; and K''n'',''n'', the complete bipartite graph with equal partite sets. 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「List edge-coloring」の詳細全文を読む スポンサード リンク
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