Galeana-Sánchez, Hortensia; Rajsbaum, Sergio Cycle-pancyclism in tournaments. II. (English) Zbl 0844.05047 Graphs Comb. 12, No. 1, 9-16 (1996). Summary: Let \(T\) be a Hamiltonian tournament with \(n\) vertices and \(\gamma\) a Hamiltonian cycle of \(T\). We develop a general method to find cycles of length \(k\) with \({n+ 4\over 2}< k< n\), intersecting \(\gamma\) in a large number of arcs. In particular we can show that if there does not exist a cycle \(C_k\) intersecting \(\gamma\) in at least \(k- 3\) arcs then for any arc \(e\) of \(\gamma\) there exists a cycle \(C_k\) containing \(e\) and intersecting \(\gamma\) in at least \(k- {2(n- 3)\over n- k+ 3}- 2\) arcs. In a previous paper [ibid. 11, No. 3, 233-243 (1995; Zbl 0833.05039)] the case of cycles of length \(k\) with \(k\leq {n+ 4\over 2}\) was studied. Cited in 1 ReviewCited in 1 Document MSC: 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles 05C45 Eulerian and Hamiltonian graphs Keywords:Hamiltonian tournament; Hamiltonian cycle Citations:Zbl 0833.05039 PDFBibTeX XMLCite \textit{H. Galeana-Sánchez} and \textit{S. Rajsbaum}, Graphs Comb. 12, No. 1, 9--16 (1996; Zbl 0844.05047) Full Text: DOI References: [1] Alspach, B.: Cycles of each length in regular tournaments. Canad. Math. Bull.10, 283–286 (1967) · Zbl 0148.43602 · doi:10.4153/CMB-1967-028-6 [2] Bermond, J.C., Thomasen, C.: Cycles in digraphs – A survey. J. Graph Theory,5, 43, 145–157 (1981) · Zbl 0458.05035 · doi:10.1002/jgt.3190050102 [3] 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.