k-Ordered Hamilton cycles in digraphs
Combinatorics
2007-07-12 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0707.1577,
title = {k-Ordered Hamilton cycles in digraphs},
author = {Daniela Kühn and Deryk Osthus and Andrew Young},
journal= {arXiv preprint arXiv:0707.1577},
year = {2007}
}