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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 Meredith graph ： ウィキペディア英語版 Meredith graph In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith in 1973. The Meredith graph is 4-vertex-connected and 4-edge-connected, has chromatic number 3, chromatic index 5, radius 7, diameter 8, girth 4 and is non-hamiltonian.〔Bondy, J. A. and Murty, U. S. R. "Graph Theory". Springer, p. 470, 2007.〕 Published in 1973, it provides a counterexample to the Crispin Nash-Williams conjecture that every 4-regular 4-vertex-connected graph is Hamiltonian.〔Meredith, G. H. J. "Regular 4-Valent 4-Connected Nonhamiltonian Non-4-Edge-Colorable Graphs." J. Combin. Th. B 14, 55-60, 1973.〕〔Bondy, J. A. and Murty, U. S. R. "Graph Theory with Applications". New York: North Holland, p. 239, 1976.〕 However, W. T. Tutte showed that all 4-connected planar graphs are hamiltonian.〔Tutte, W.T., ed., Recent Progress in Combinatorics. Academic Press, New York, 1969.〕 The characteristic polynomial of the Meredith graph is $(x-4)\; (x-1)^\; x^\; (x+1)^\; (x+3)\; (x^2-13)\; (x^6-26\; x^4+3\; x^3+169\; x^2-39\; x-45)^4$. ==Gallery== Image:Meredith graph 3COL.svg|The chromatic number of the Meredith graph is 3. Image:Meredith graph 5color edge.svg|The chromatic index of the Meredith graph is 5. 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「Meredith graph」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.