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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Robbins' theorem ： ウィキペディア英語版 Robbins' theorem In graph theory, Robbins' theorem, named after , states that the graphs that have strong orientations are exactly the 2-edge-connected graphs. That is, it is possible to choose a direction for each edge of an undirected graph , turning into a directed graph that has a path from every vertex to every other vertex, if and only if is connected and has no bridge. ==Orientable graphs== Robbins' characterization of the graphs with strong orientations may be proven using ear decomposition, a tool introduced by Robbins for this task. If a graph has a bridge, then it cannot be strongly orientable, for no matter which orientation is chosen for the bridge there will be no path from one of the two endpoints of the bridge to the other. In the other direction, it is necessary to show that every connected bridgeless graph can be strongly oriented. As Robbins proved, every such graph has a partition into a sequence of subgraphs called "ears", in which the first subgraph in the sequence is a cycle and each subsequent subgraph is a path, with the two path endpoints both belonging to earlier ears in the sequence. Orienting the edges within each ear so that it forms a directed cycle or a directed path leads to a strongly connected orientation of the overall graph.〔.〕 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「Robbins' theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.