An upper bound on the size of the snake-in-the-box

Abstract

A snake in a graph is a simple cycle without chords. We give an upper bound on the size of a snake S in then-dimensional cube of the form |S|≤2n−1(1−n 1/2/89+O(1/n)).

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References

  1. [1]

    H. L. Abbot: Some Problems in Combinatorial Analysis, PhD thesis, University of Alberta, Edmonton, Canada, 1965.

    Google Scholar 

  2. [2]

    H. L. Abbot andM. Katchalski: On the construction of snake in the box codes,Utilitas Mathematica,40 (1991), 97–116.

    Google Scholar 

  3. [3]

    L. Danzer andV. Klee: Length of snakes in boxes,J. Combin. Theory,2 (1967), 258–265.

    Google Scholar 

  4. [4]

    K. Deimer: A new upper bound for the length of snakes,Combinatorica,5 (1985), 109–120.

    Google Scholar 

  5. [5]

    R. J. Douglas: Upper bounds on the length of circuits of even spread in thed-cube,J. Combin. Theory,7 (1969), 206–214.

    Google Scholar 

  6. [6]

    A. A. Evdomikov: Maximal length of a circuit in a unitaryn-dimensional cube,Mat. Zametki,6 (1969), 309–329.

    Google Scholar 

  7. [7]

    V. V. Glagolev: An upper estimate of the length of a cycle in then-dimensional unit cube,Diskretnyi Analiz,6 (1966), 3–7.

    Google Scholar 

  8. [8]

    W. H. Kautz: Unit distance error checking codes,IRE Trans. Electron. Comput.,7 (1958), 179–180.

    Google Scholar 

  9. [9]

    D. G. Larman: Circuit codes. quoted from [5],, 1968.

    Google Scholar 

  10. [10]

    R. C. Singleton: Generalized snake-in-the-box codes,IEEE Trans. Electronic Computers, EC-15 (1966), 596–602.

    Google Scholar 

  11. [11]

    H. S. Snevily: The snake-in-the-box problem: A new upper bound,Discrete Math.,133 (1994), 307–314.

    Google Scholar 

  12. [12]

    F. I. Solov'jeva: An upper bound for the length of a cycle in ann-dimensional unit cube,Diskretnyi Analiz,45 (1987).

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Zémor, G. An upper bound on the size of the snake-in-the-box. Combinatorica 17, 287–298 (1997). https://doi.org/10.1007/BF01200911

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Mathematics Subject Classification (1991)

  • 05C38
  • 68R10
  • 94B60
  • 94B65