Geodesic
Cycle-pancyclism in bipartite tournaments I
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 277-290.

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Let T be a hamiltonian bipartite tournament with n vertices, γ a hamiltonian directed cycle of T, and k an even number. In this paper, the following question is studied: What is the maximum intersection with γ of a directed cycle of length k? It is proved that for an even k in the range 4 ≤ k ≤ [(n+4)/2], there exists a directed cycle C_h(k) of length h(k), h(k) ∈ k,k-2 with |A(C_h(k)) ∩ A(γ)| ≥ h(k)-3 and the result is best possible.
Keywords: bipartite tournament, pancyclism 
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Galeana-Sánchez, Hortensia. Cycle-pancyclism in bipartite tournaments I. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 277-290. http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a9/

[1] B. Alpach, Cycles of each length in regular tournaments, Canad. Math. Bull. 10 (1967) 283-286, doi: 10.4153/CMB-1967-028-6.

[2] L.W. Beineke, A tour through tournaments or bipartite and ordinary tournaments: A comparative survey, J. London Math. Soc., Lect. Notes Ser. 52 (1981) 41-55.

[3] L.W. Beineke and V. Little, Cycles in bipartite tournaments, J. Combin. Theory (B) 32 (1982) 140-145, doi: 10.1016/0095-8956(82)90029-6.

[4] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1976).

[5] J.C. Bermond and C. Thomasen, Cycles in digraphs - A survey, J. Graph Theory 5 (43) (1981) 145-147.

[6] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments I, Graphs and Combin. 11 (1995) 233-243, doi: 10.1007/BF01793009.

[7] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments II, Graphs and Combin. 12 (1996) 9-16, doi: 10.1007/BF01858440.

[8] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments III, Graphs and Combin. 13 (1997) 57-63, doi: 10.1007/BF01202236.

[9] H. Galeana-Sánchez and S. Rajsbaum, A Conjecture on Cycle-Pancyclism in Tournaments, Discuss. Math. Graph Theory 18 (1998) 243-251, doi: 10.7151/dmgt.1080.

[10] G. Gutin, Cycles and paths in semicomplete multipartite digraphs, theorems and algorithms: A survey, J. Graph Theory 19 (1995) 481-505, doi: 10.1002/jgt.3190190405.

[11] R. Häggkvist and Y. Manoussakis, Cycles and paths in bipartite tournaments with spanning configurations, Combinatorica 9 (1989) 33-38, doi: 10.1007/BF02122681.

[12] L. Volkmann, Cycles in multipartite tournaments, results and problems, Discrete Math. 245 (2002) 19-53, doi: 10.1016/S0012-365X(01)00419-8.

[13] C.Q. Zhang, Vertex even-pancyclicity in bipartite tournaments, J. Nanjing Univ. Math., Biquart 1 (1981) 85-88.

[14] K.M. Zhang and Z.M. Song, Cycles in digraphs, a survey, J. Nanjing Univ., Nat. Sci. Ed. 27 (1991) 188-215.