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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
##### Keywords:
arc-parcyclic; tournaments; scores
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##### References:
 [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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