A simple circuit in the -Hypercube which has no chords (i.e., for which all snake edges are edges of the
Hypercube). Klee (1970) asked for the maximum length of a -snake. Klee (1970) gave the bounds
(1) |
(2) |
(3) |
(4) |
See also Hypercube
References
Abbott, H. L. and Katchalski, M. ``On the Snake in the Box Problem.'' J. Combin. Th. Ser. B 44, 12-24, 1988.
Danzer, L. and Klee, V. ``Length of Snakes in Boxes.'' J. Combin. Th. 2, 258-265, 1967.
Douglas, R. J. ``Some Results on the Maximum Length of Circuits of Spread in the -Cube.'' J. Combin. Th.
6, 323-339, 1969.
Evdokimov, A. A. ``Maximal Length of a Chain in a Unit -Dimensional Cube.'' Mat. Zametki 6, 309-319, 1969.
Guy, R. K. ``Unsolved Problems Come of Age.'' Amer. Math. Monthly 96, 903-909, 1989.
Kautz, W. H. ``Unit-Distance Error-Checking Codes.'' IRE Trans. Elect. Comput. 7, 177-180, 1958.
Klee, V. ``What is the Maximum Length of a -Dimensional Snake?'' Amer. Math. Monthly 77, 63-65, 1970.
Sloane, N. J. A. Sequence
A000937/M0995
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
Snevily, H. S. ``The Snake-in-the-Box Problem: A New Upper Bound.'' Disc. Math. 133, 307-314, 1994.
© 1996-9 Eric W. Weisstein