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An Upper Bound for the Length of a Snake in the n-Dimensional Unit Cube

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Operations Research and Discrete Analysis

Part of the book series: Mathematics and Its Applications ((MAIA,volume 391))

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Abstract

By refining some details of the proof in the paper [1], a more precise bound is obtained for the length of an arbitrary snake in the n-dimensional unit cube.

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References

  1. H. S. Snevily (1994) The snake-in-the-box problem: A new upper bound, Dis crete Math. 133, No. 1-3, 307–314.

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  2. F. I. Solov’ëva (1987) An upper bound on the length of a cycle in the n-di-mensional unit cube (in Russian), Metody Diskret. Anal. 45, 71–76.

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  3. A. A. Evdokimov and S. A. Malyugin (1987) The “snake-in-the-box” code and paths in a lattice on a torus (in Russian), Mathematics Today, Vishcha Shkola, Kiev, pp. 108–116.

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  4. K. Deimer (1985) A new upper bound for the length of snakes, Combinatorica 5, No. 2, 109–120.

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  5. H. L. Abbot and M. Katchalski (1991) On the construction of a snake in the box codes, Utilitas Math. 40, 97–116.

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  6. A. A. Evdokimov (1990) Embedding of chains and cycles in a hypercube. I (in Russian), Metody Diskret. Anal. 50, 10–25.

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© 1997 Springer Science+Business Media Dordrecht

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Emel′yanov, P.G. (1997). An Upper Bound for the Length of a Snake in the n-Dimensional Unit Cube. In: Operations Research and Discrete Analysis. Mathematics and Its Applications, vol 391. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5678-3_4

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  • DOI: https://doi.org/10.1007/978-94-011-5678-3_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6395-1

  • Online ISBN: 978-94-011-5678-3

  • eBook Packages: Springer Book Archive

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