论文信息 - Enumeration of Hamiltonian Cycles in 6-cube

Enumeration of Hamiltonian Cycles in 6-cube

Finding the number 2H6 of directed Hamiltonian cycles in 6-cube is problem 43 in Section 7.2.1.1 of Knuth's ' The Art of Computer Programming'; various proposed estimates are surveyed below. We computed exact value: H6=14,754,666,508,334,433,250,560=6*2^4*217,199*1,085,989*5,429,923. Also the number Aut6 of those cycles up to automorphisms of 6-cube was computed as 147,365,405,634,413,085

Michel Deza | Roman Shklyar | M. Deza | R. Shklyar

[1] Robert James Douglas,et al. Bounds on the number of Hamiltonian circuits in the n-cube , 1977, Discret. Math..

[2] S. Goodman,et al. On the number of Hamiltonian circuits in the $n$-cube , 1975 .

[3] Tomás Feder,et al. Nearly tight bounds on the number of Hamiltonian circuits of the hypercube and generalizations , 2009, Inf. Process. Lett..

[4] Italo J. Dejter,et al. Classes of Hamilton Cycles in the 5-Cube , 2022 .

[5] E. Gilbert. Gray codes and paths on the N-cube , 1958 .

[6] David Thomas,et al. The Art in Computer Programming , 2001 .

[7] N. J. A. Sloane,et al. The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[8] P. P. Parkhomenko. Classification of the Hamiltonian Cycles in Binary Hypercubes , 2001 .

[9] Donald Ervin Knuth,et al. The Art of Computer Programming , 1968 .

[10] Daniel Kroening,et al. Towards a Classification of Hamiltonian Cycles in the 6-Cube , 2008, Journal on Satisfiability, Boolean Modeling and Computation.

[11] V. E. Vickers,et al. Statistical estimates of the n-bit Gray codes by restricted random generation of permutations of 1 to 2n , 1983, IEEE Trans. Inf. Theory.