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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 Gale–Ryser theorem ： ウィキペディア英語版 Gale–Ryser theorem The Gale–Ryser theorem is a result in graph theory and combinatorial matrix theory, two branches of combinatorics. It provides one of two known approaches solving the bipartite realization problem, i.e. it gives a necessary and sufficient condition for two finite sequences of natural numbers to be the degree sequence of a labeled simple bipartite graph;a sequence obeying these conditions is called "bigraphic". It is an analog of the Erdős–Gallai theorem for simple graphs. The theorem was published in 1957 by H. J. Ryser and also by David Gale. ==Theorem statement== A pair of sequences of nonnegative integers $(a\_1,\backslash ldots,a\_n)$ and $(b\_1,\backslash ldots,b\_n)$ with $a\_1\backslash geq\backslash cdots\backslash geq\; a\_n$ is bigraphic if and only if $\backslash sum\_^a\_i=\backslash sum\_^b\_i$ and the following inequality holds for k such that $1\; \backslash leq\; k\; \backslash leq\; n$: :$$ \sum^k_ a_i\leq \sum^n_ \min(b_i,k). 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「Gale–Ryser 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.