Graphs and Combinatorics

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

Cycle-pancyclism in tournaments I

  • Hortensia Galeana-Sánchez
  • Sergio Rajsbaum
Original Papers


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.


Maximum Intersection Hamiltonian Cycle Forthcoming Paper 


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  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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