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 ≤k ≤n + 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.
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Bermond, J.C., Thomasen, C.: Cycles in digraphs — A survey. J. Graph Theory,5, 43, 145–157 (1981)
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On leave at the MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139.
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Galeana-Sánchez, H., Rajsbaum, S. Cycle-pancyclism in tournaments I. Graphs and Combinatorics 11, 233–243 (1995). https://doi.org/10.1007/BF01793009
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DOI: https://doi.org/10.1007/BF01793009