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Linkedness and Ordered Cycles in Digraphs

Published online by Cambridge University Press:  01 May 2008

DANIELA KÜHN  and
DERYK OSTHUS
DANIELA KÜHN
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk)
DERYK OSTHUS
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk)
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Abstract

Given a digraph D, let δ0(D) := min{δ+(D), δ−(D)} be the minimum semi-degree of D. We show that every sufficiently large digraph D with δ0(D)≥n/2 + l −1 is l-linked. The bound on the minimum semi-degree is best possible and confirms a conjecture of Manoussakis [17]. We also determine the smallest minimum semi-degree which ensures that a sufficiently large digraph D is k-ordered, i.e., that for every sequence s1, . . ., sk of distinct vertices of D there is a directed cycle which encounters s1, . . ., sk in this order. This result will be used in [16].

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 3 , May 2008 , pp. 411 - 422
Copyright
Copyright © Cambridge University Press 2007

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