Abstract
LetT be a Hamiltonian tournament withn vertices andγ a Hamiltonian cycle ofT. In this paper we develope a general method to find cycles of lengthk, n+4/2 < k < n, intersectingγ in a large number of arcs. In particular we can show that if there does not exist a cycle.C k intersectingγ in at leastk − 3 arcs then for any arce ofγ there exists a cycleC k containinge and intersectingγ in at leastk − 2(n−3)/n−k+3 − 2 arcs. In a previous paper [3] the case of cycles of lengthk, k ≤ n+4/2 was studied.
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Alspach, B.: Cycles of each length in regular tournaments. Canad. Math. Bull.10, 283–286 (1967)
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Galeana-Sanchez, H., Rajsbaum, S.: Cycle Pancyclism in Tournaments I, Pub. Prel. 266 (technical report), Instituto de Matemáticas, UNAM, Mexico, April 1992. Submitted for publication
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On leave at MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139, USA.
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Galeana-Sánchez, H., Rajsbaum, S. Cycle-pancyclism in tournaments II. Graphs and Combinatorics 12, 9–16 (1996). https://doi.org/10.1007/BF01858440
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DOI: https://doi.org/10.1007/BF01858440