中间层猜想（Havel 1983，Buck 和 Wiedemann 1984），也称为旋转门猜想，假设阶数为 
的中间层图对于每个 
都存在哈密顿环。
该猜想已由 Mütze (2016) 证明；另见 Mütze (2024)。
由于中间层图是顶点传递的，证明该猜想确定了这些图不是 Thomassen 关于非哈密顿顶点传递图的猜想的反例。
Knuth (2021) 在他的书中（Mütze 2024）给中间层猜想在所有未解决问题中最高的难度评级（49/50）。
中间层猜想
另请参阅
哈密顿环, 中间层图, 顶点传递图使用 Wolfram|Alpha 探索
参考文献
Buck, M. and Wiedemann, D. "Gray Codes With Restricted Density." Disc. Math. 48, 163-171, 1984.Diaconis, P. and Graham, R. Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks. Princeton, NJ: Princeton UNiversity Press, 2011.Felsner, S. and Trotter, W. T. "Colorings of Diagrams of Interval Orders and
-Sequences of Sets." Disc. Math. 144, 23-31, 1995.Havel, I. "Semipaths in Directed Cubes." In Graphs and Other Combinatorial Topics (Prague, 1982). Leipzig, Germany: Teubner, pp. 101-108, 1983.Kierstead, H. A. and Trotter, W. T. "Explicit Matchings in the Middle Levels of the Boolean Lattice." Order 5, 163-171, 1988.Knuth, D. E. The Art of Computer Programming, Vol. 4A: Combinatorial Algorithms, Part 1. New York: Addison-Wesley, 2021.Mütze, T. "Proof of the Middle Levels Conjecture." 11 Aug 2014. https://arxiv.org/abs/1404.4442.Mütze, T. "On Hamilton Cycles in Graphs Defined by Intersecting Set Systems." Not. Amer. Soc. 74, 583-592, 2024.Savage, C. D. and Winkler, P. "Monotone Gray Codes and the Middle Levels Problem." J. Combin. Th. Ser. A 70, 230-248, 1995.Winkler, P. Mathematical Puzzles. Boca Raton, FL: CRC Press, 2003.
引用为
Weisstein, Eric W. "中间层猜想。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/MiddleLevelsConjecture.html