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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 Erdős–Stone theorem ： ウィキペディア英語版 Erdős–Stone theorem In extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an ''H''-free graph for a non-complete graph ''H''. It is named after Paul Erdős and Arthur Stone, who proved it in 1946, and it has been described as the “fundamental theorem of extremal graph theory”. ==Extremal functions of Turán graphs== The extremal function ex(''n''; ''H'') is defined to be the maximum number of edges in a graph of order ''n'' not containing a subgraph isomorphic to ''H''. Turán's theorem says that ex(''n''; ''K''''r'') = ''t''''r'' − 1(''n''), the order of the Turán graph, and that the Turán graph is the unique extremal graph. The Erdős–Stone theorem extends this to graphs not containing ''K''''r''(''t''), the complete ''r''-partite graph with ''t'' vertices in each class (equivalently the Turán graph ''T''(''rt'',''r'')): :$\backslash mbox(n;\; K\_r(t))\; =\; \backslash left(\; \backslash frac\; +\; o(1)\; \backslash right).$ 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「Erdős–Stone 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.