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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 Havel–Hakimi algorithm ： ウィキペディア英語版 Havel–Hakimi algorithm The Havel–Hakimi algorithm is an algorithm in graph theory solving the graph realization problem, i.e. the question if there exists for a finite list of nonnegative integers a simple graph such that its degree sequence is exactly this list. For a positive answer the list of integers is called ''graphic''. The algorithm constructs a special solution if one exists or proves that one cannot find a positive answer. This construction is based on a recursive algorithm. The algorithm was published by , and later by . ==The algorithm== The algorithm is based on the following theorem. Let $S=(d\_1,\backslash dots,d\_n)$ be a finite list of nonnegative integers that is nonincreasing. List $S$ is graphic if and only if the finite list $S\text{'}=(d\_2-1,d\_3-1,\backslash dots,d\_-1,d\_,\backslash dots,d\_n)$ has nonnegative integers and is graphic. Is the given list $S$ graphic then the theorem will be applied at most $n-1$ times setting in each further step $S:=S\text{'}$. Note that it can be necessary to sort this list again. This process ends when the whole list $S\text{'}$ consists of zeros. In each step of the algorithm one constructs the edges of a graph with vertices $v\_1,\backslash cdots,v\_n$, i.e. if it is possible to reduce the list $S$ to $S\text{'}$, then we add edges $\backslash ,\backslash ,\backslash cdots,\backslash$. When the list $S$ cannot be reduced to a list $S\text{'}$ of nonnegative integers in any step of this approach, the theorem proves that the list $S$ from the beginning is not graphic. 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「Havel–Hakimi algorithm」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.