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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 Expander mixing lemma ： ウィキペディア英語版 Expander mixing lemma The expander mixing lemma states that, for any two subsets $S,\; T$ of a d-regular expander graph $G$ with $n$ vertices, the number of edges between $S$ and $T$ is approximately what you would expect in a random ''d''-regular graph, i.e. $d|S|\; |T|\; /\; n$. ==Statement== Let $G\; =\; (V,\; E)$ be a ''d''-regular graph on ''n'' vertices with $\backslash lambda\backslash in(0,1)$ the second-largest eigenvalue (in absolute value) of the normalized adjacency matrix. For any two subsets $S,\; T\; \backslash subseteq\; V$, let $E(S,\; T)\; =\; |\backslash |$ be the number of edges between ''S'' and ''T'' (counting edges contained in the intersection of ''S'' and ''T'' twice). Then :$\backslash left|E(S,\; T)\; -\; \backslash frac\backslash right|\; \backslash leq\; d\; \backslash lambda\; \backslash sqrt\backslash ,.$ 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「Expander mixing lemma」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.