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Bypaths in tournaments. (English) Zbl 0882.05080

Let \(T\) be a tournament of order \(n\). If \(T\) is 3-connected and each arc of \(T\) is contained in a cycle of length 3, then every arc of \(T\) has a bypath of length \(k\), for each \(k\) with \(3 \leq k \leq n-1\), unless \(T\) is isomorphic to two tournaments, each of which is of order 8.

MSC:

05C38 Paths and cycles
05C20 Directed graphs (digraphs), tournaments
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References:

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