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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 Edmonds matrix ： ウィキペディア英語版 Edmonds matrix In graph theory, the Edmonds matrix $A$ of a balanced bipartite graph $G(U,\; V,\; E)$ with sets of vertices $U\; =\; \backslash$ and $V\; =\; \backslash$ is defined by :$A\_\; =\; \backslash left\backslash$ x_ & (u_i, v_j) \in E \\ 0 & (u_i, v_j) \notin E \end\right. where the ''x''ij are indeterminates. One application of the Edmonds matrix of a bipartite graph is that the graph admits a perfect matching if and only if the polynomial det(''A''ij) in the ''x''ij is not identically zero. Furthermore, the number of perfect matchings is equal to the number of monomials in the polynomial det(''A''), and is also equal to the permanent of $A$. In addition, rank of $A$ is equal to the maximum matching size of $G$. The Edmonds matrix is named after Jack Edmonds. The Tutte matrix is a generalisation to non-bipartite graphs. ==References== * * 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「Edmonds matrix」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.