中間層猜想（Havel 1983，Buck 和 Wiedemann 1984），也稱為旋轉門猜想，假設階數為 
的中間層圖對於每個 
都存在哈密頓環。
該猜想已由 Mütze (2016) 證明；另見 Mütze (2024)。
由於中間層圖是頂點傳遞的，證明該猜想確定了這些圖不是 Thomassen 關於非哈密頓頂點傳遞圖的猜想的反例。
Knuth (2021) 在他的書中（Mütze 2024）給中間層猜想在所有未解決問題中最高的難度評級（49/50）。
中間層猜想
另請參閱
哈密頓環, 中間層圖, 頂點傳遞圖使用 探索
參考文獻
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.
引用為
Weisstein, Eric W. "中間層猜想。" 來自 Web 資源。 https://mathworld.tw/MiddleLevelsConjecture.html