k-Ordered Hamilton cycles in digraphs

Details k-Ordered Hamilton cycles in digraphs k-Ordered Hamilton cycles in digraphs

2007-07-11

arxiv.org/abs/0707.1577v1

Mathematics

Combinatorics

Scientific paper

Given a digraph D, the minimum semi-degree of D is the minimum of its minimum indegree and its minimum outdegree. D is k-ordered Hamiltonian if for every ordered sequence of k distinct vertices there is a directed Hamilton cycle which encounters these vertices in this order. Our main result is that every digraph D of sufficiently large order n with minimum semi-degree at least (n+k)/2 -1 is k-ordered Hamiltonian. The bound on the minimum semi-degree is best possible. An undirected version of this result was proved earlier by Kierstead, S\'ark\"ozy and Selkow.

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