翻訳と辞書 Words near each other ・ Kurdish National Congress ・ Kurdish National Council ・ Kurdish nationalism ・ Kurdish News Network ・ Kurate, Fukuoka ・ Kurathi Magan ・ Kuratite ・ Kuratong Baleleng ・ Kuratov ・ Kuratowski and Ryll-Nardzewski measurable selection theorem ・ Kuratowski closure axioms ・ Kuratowski convergence ・ Kuratowski embedding ・ Kuratowski's closure-complement problem ・ Kuratowski's free set theorem ・ Kuratowski's theorem ・ Kuratowski–Ulam theorem ・ Kurattikkadu ・ Kurattissery ・ Kurau Phantom Memory ・ Kurauchi Station ・ Kuraulyek ・ Kurauni ・ Kuravan Palayam ・ Kuravanji ・ Kuravanmala ・ Kuravar ・ Kuravi ・ Kuravilangad ・ Kuravinakoppa 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 Kuratowski's theorem ： ウィキペディア英語版 Kuratowski's theorem In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states that a finite graph is planar if and only if it does not contain a subgraph that is a subdivision of ''K''5 (the complete graph on five vertices) or of ''K''3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three, also known as the utility graph). ==Statement of the theorem== A planar graph is a graph whose vertices can be represented by points in the Euclidean plane, and whose edges can be represented by simple curves in the same plane connecting the points representing their endpoints, such that no two curves intersect except at a common endpoint. Planar graphs are often drawn with straight line segments representing their edges, but by Fáry's theorem this makes no difference to their graph-theoretic characterization. A subdivision of a graph is a graph formed by subdividing its edges into paths of one or more edges. Kuratowski's theorem states that a finite graph ''G'' is planar, if it is not possible to subdivide the edges of ''K''5 or ''K''3,3, and then possibly add additional edges and vertices, to form a graph isomorphic to ''G''. Equivalently, a finite graph is planar if and only if it does not contain a subgraph that is homeomorphic to ''K''5 or ''K''3,3. 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「Kuratowski's 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.