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塔特猜想

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塔特 (1971/72) 猜想不存在 3-連通的非哈密頓量雙三次圖。然而，J. D. Horton 在 1976 年 (Gropp 1990) 找到了一個反例，現在已知幾個更小的反例。

NonhamiltonianBicubicGraphs

已知的小反例總結在下表中並在上方進行了說明。

V名稱參考
50Georges 圖Georges (1989), Grünbaum (2006, 2009)
54Ellingham-Horton 54-圖Ellingham 和 Horton (1983)
78Ellingham-Horton 78-圖Ellingham (1981, 1982)
78Owens 圖Owens (1983)
92Horton 92-圖Horton (1982)
96Horton 96-圖Bondy 和 Murty (1976)

參見

雙三次圖, 雙三次非哈密頓量圖, 三次圖, Ellingham-Horton 圖, Georges 圖, Horton 圖, 非哈密頓量圖, Tait 的哈密頓圖猜想

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參考資料

Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, pp. 61 and 242, 1976.Bondy, J. A. and Murty, U. S. R. Graph Theory. Berlin: Springer-Verlag, pp. 487-488, 2008.Ellingham, M. N. "Non-Hamiltonian 3-Connected Cubic Partite Graphs." Research Report No. 28, Dept. of Math., Univ. Melbourne, Melbourne, 1981.Ellingham, M. N. "Constructing Certain Cubic Graphs." In Combinatorial Mathematics, IX: Proceedings of the Ninth Australian Conference held at the University of Queensland, Brisbane, August 24-28, 1981 (Ed. E. J. Billington, S. Oates-Williams, and A. P. Street). Berlin: Springer-Verlag, pp. 252-274, 1982.Ellingham, M. N. and Horton, J. D. "Non-Hamiltonian 3-Connected Cubic Bipartite Graphs." J. Combin. Th. Ser. B 34, 350-353, 1983.Georges, J. P. "Non-Hamiltonian Bicubic Graphs." J. Combin. Th. B 46, 121-124, 1989.Gropp, H. "Configurations and the Tutte Conjecture." Ars. Combin. A 29, 171-177, 1990.Grünbaum, B. "3-Connected Configurations (n_3) with No Hamiltonian Circuit." Bull. Inst. Combin. Appl. 46, 15-26, 2006.Grünbaum, B. Configurations of Points and Lines. Providence, RI: Amer. Math. Soc., p. 311, 2009.Horton, J. D. "On Two-Factors of Bipartite Regular Graphs." Disc. Math. 41, 35-41, 1982.Owens, P. J. "Bipartite Cubic Graphs and a Shortness Exponent." Disc. Math. 44, 327-330, 1983.Tutte, W. T. "On the 2-Factors of Bicubic Graphs." Disc. Math. 1, 203-208, 1971/72.

在 中被引用

塔特猜想

引用為

Weisstein, Eric W. "塔特猜想。" 來自 Web 資源。 https://mathworld.tw/TutteConjecture.html

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