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Graphs and Combinatorics

, Volume 11, Issue 3, pp 233–243 | Cite as

Cycle-pancyclism in tournaments I

  • Hortensia Galeana-Sánchez
  • Sergio Rajsbaum
Original Papers

Abstract

LetT be a hamiltonian tournament withn vertices andγ a hamiltonian cycle ofT. In this paper we start the study of the following question: What is the maximum intersection withγ of a cycle of lengthk? This number is denotedf(n, k). We prove that fork in range, 3 ≤kn + 4/2,f(n,k) ≥ k − 3, and that the result is best possible; in fact, a characterization of the values ofn, k, for whichf(n, k) = k − 3 is presented.

In a forthcoming paper we studyf(n, k) for the case of cycles of lengthk > n + 4/2.

Keywords

Maximum Intersection Hamiltonian Cycle Forthcoming Paper 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alspach, B.: Cycles of each length in regular tournaments, Canadian Math. Bull.,10, 283–286 (1967)Google Scholar
  2. 2.
    Bermond, J.C., Thomasen, C.: Cycles in digraphs — A survey. J. Graph Theory,5, 43, 145–157 (1981)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Hortensia Galeana-Sánchez
    • 1
  • Sergio Rajsbaum
    • 1
  1. 1.Instituto de MatemáticasU.N.A.M., C.U.Circuito ExteriorMéxico

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