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Hamiltonian dicycles avoiding prescribed arcs in tournaments. (English) Zbl 0622.05028
The main result of this paper is the following theorem: If T is a k- connected tournament and I a set of k-1 arcs of T, then T-I has a Hamiltonian directed cycle.
This result was conjectured by the second author in a previous paper [Proc. Lond. Math. Soc., III. Ser. 45, 151-168 (1982; Zbl 0486.05049)].
Reviewer: I.Tomescu

MSC:
05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C45 Eulerian and Hamiltonian graphs
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[1] Camion, P.: Chemins et circuits hamiltoniens des graphes complets. C.R. Acad. Sci. Paris249, 2151–2152 (1959) · Zbl 0092.15801
[2] Thomassen, C.: Hamiltonian-connected tournaments. J. Comb. Theory (B)28, 142–163 (1980) · Zbl 0435.05026 · doi:10.1016/0095-8956(80)90061-1
[3] Thomassen, C.: Edge – disjoint Hamiltonian paths and cycles in tournaments. Proc. London Math. Soc.45, 151–168 (1982). · Zbl 0486.05049 · doi:10.1112/plms/s3-45.1.151
[4] Thomassen, C.: Connectivity in tournaments. In: Graph Theory and Combinatorics (B. Bollobás, ed.) pp. 305–313. London: Academic Press 1984
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