翻訳と辞書 Words near each other ・ Erdőkertes ・ Erdőkürt ・ Erdős ・ Erdős arcsine law ・ Erdős cardinal ・ Erdős conjecture on arithmetic progressions ・ Erdős distinct distances problem ・ Erdős number ・ Erdős Prize ・ Erdős space ・ Erdősmecske ・ Erdősmárok ・ Erdős–Anning theorem ・ Erdős–Bacon number ・ Erdős–Borwein constant ・ Erdős–Burr conjecture ・ Erdős–Diophantine graph ・ Erdős–Faber–Lovász conjecture ・ Erdős–Fuchs theorem ・ Erdős–Gallai theorem ・ Erdős–Graham problem ・ Erdős–Gyárfás conjecture ・ Erdős–Hajnal conjecture ・ Erdős–Kac theorem ・ Erdős–Ko–Rado theorem ・ Erdős–Mordell inequality ・ Erdős–Nagy theorem ・ Erdős–Nicolas number ・ Erdős–Pósa theorem ・ Erdős–Rado theorem Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Erdős–Burr conjecture ： ウィキペディア英語版 Erdős–Burr conjecture In mathematics, the Erdős–Burr conjecture is a problem concerning the Ramsey number of sparse graphs. The conjecture is named after Paul Erdős and Stefan Burr, and is one of many conjectures named after Erdős; it states that the Ramsey number of graphs in any sparse family of graphs should grow linearly in the number of vertices of the graph. In 2015, a proof of the conjecture was announced by Choongbum Lee.〔; 〕 ==Definitions== If ''G'' is an undirected graph, then the degeneracy of ''G'' is the minimum number ''p'' such that every subgraph of ''G'' contains a vertex of degree ''p'' or smaller. A graph with degeneracy ''p'' is called ''p''-degenerate. Equivalently, a ''p''-degenerate graph is a graph that can be reduced to the empty graph by repeatedly removing a vertex of degree ''p'' or smaller. It follows from Ramsey's theorem that for any graph ''G'' there exists a least integer $r(G)$, the ''Ramsey number'' of ''G'', such that any complete graph on at least $r(G)$ vertices whose edges are coloured red or blue contains a monochromatic copy of ''G''. For instance, the Ramsey number of a triangle is 6: no matter how the edges of a complete graph on six vertices are colored red or blue, there is always either a red triangle or a blue triangle. 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–Burr conjecture」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.