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Arc-pancyclic property of tournaments under some degree conditions. (English) Zbl 0534.05032
Let s(u) denote the score of node u in a tournament \(T_ n\) with n nodes. Suppose there exists an integer q such that \(s(u)\leq s(v)+q-1\) for every arc \(u\vec v\) in \(T_ n\). The authors show that if \(3q+3\leq p\) then each arc of \(T_ n\) is contained in a k-cycle for each integer k such that \(5\leq k\leq n.\)
Reviewer: J.W.Moon

MSC:
05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
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[1] Alspach B., Cand. Math. Bull. 10 pp 283– (1967) · Zbl 0148.43602 · doi:10.4153/CMB-1967-028-6
[2] Zhu Y.J., Scientia Sinica, Special Issue pp 18– (1979)
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