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Highly connected non-2-linked digraphs. (English) Zbl 0746.05030
A digraph \(D\) is said to be 2-linked if for any four vertices \(x_ 1\), \(x_ 2\), \(y_ 1\), and \(y_ 2\) there exist disjoint directed paths \(P_ 1\) and \(P_ 2\) starting at \(x_ 1\) and \(x_ 2\) and ending at \(y_ 1\) and \(y_ 2\), respectively. The author shows that for every positive integers \(k\) there exists a strongly \(k\)-connected digraph \(D\) that is not 2-linked.

MSC:
05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C40 Connectivity
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