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On the number of Hamiltonian circuits in the $ n$-cube

Authors: E. Dixon and S. Goodman
Journal: Proc. Amer. Math. Soc. 50 (1975), 500-504
MSC: Primary 05C35
MathSciNet review: 0369157
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Abstract: Improved upper and lower bounds are found for the number of hamiltonian circuits in the $ n$-cube.

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  • [1] V. Klee, Long paths and circuits on polytopes, Convex Polytopes, Pure and Appl. Math., vol. 16, Interscience, New York, 1967, pp. 356-389. MR 37 #2085. MR 0226496 (37:2085)
  • [2] E. N. Gilbert, Gray codes and paths on the $ n$-cube, Bell System Tech. J. 37 (1958), 815-826. MR 20 #792. MR 0094273 (20:792)
  • [3] R. J. Douglas, A note on a theorem of H. L. Abbott, Canad. Math. Bull. 13 (1970), 79-81. MR 43 #6117. MR 0280397 (43:6117)
  • [4] H. L. Abbott, Hamiltonian circuits and paths on the $ n$-cube, Canad. Math. Bull. 9 (1966), 557-562. MR 34 #7395. MR 0207580 (34:7395)
  • [5] E. Dixon and S. Goodman, An algorithm for finding all the hamiltonian circuits and two factors in an arbitrary directed or undirected graph, DAMACS Tech. Rept., 3-73, University of Virginia, Charlottsville, Va., 1973.
  • [6] E. N. Gilbert, Private communication.

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Keywords: Hamiltonian circuit, $ n$-cube, undirected graph, edge, node
Article copyright: © Copyright 1975 American Mathematical Society

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