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arXiv · 0704.0211

Linkedness and ordered cycles in digraphs

Daniela Kühn·Deryk Osthus
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Abstract

The minimum semi-degree of a digraph D is the minimum of its minimum outdegree and its minimum indegree. We show that every sufficiently large digraph D with minimum semi-degree at least n/2 +k-1 is k-linked. The bound on the minimum semi-degree is best possible and confirms a conjecture of Manoussakis from 1990. We also determine the smallest minimum semi-degree which ensures that a sufficiently large digraph D is k-ordered, i.e. that for every ordered sequence of k distinct vertices of D there is a directed cycle which encounters these vertices in this order.

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Daniela Kühn, Deryk Osthus. 2007-04-02. Linkedness and ordered cycles in digraphs. https://arxiv.org/abs/0704.0211

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