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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 Chromatic polynomial ： ウィキペディア英語版 Chromatic polynomial The chromatic polynomial is a polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to attack the four color problem. It was generalised to the Tutte polynomial by H. Whitney and W. T. Tutte, linking it to the Potts model of statistical physics. ==History== George David Birkhoff introduced the chromatic polynomial in 1912, defining it only for planar graphs, in an attempt to prove the four color theorem. If $P(G,\; k)$ denotes the number of proper colorings of ''G'' with ''k'' colors then one could establish the four color theorem by showing $P(G,\; 4)>0$ for all planar graphs ''G''. In this way he hoped to apply the powerful tools of analysis and algebra for studying the roots of polynomials to the combinatorial coloring problem. Hassler Whitney generalised Birkhoff’s polynomial from the planar case to general graphs in 1932. In 1968 Read asked which polynomials are the chromatic polynomials of some graph, a question that remains open, and introduced the concept of chromatically equivalent graphs. Today, chromatic polynomials are one of the central objects of algebraic graph theory.〔Several chapters 〕 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「Chromatic polynomial」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.