Linkedness and ordered cycles in digraphs

Authors:
Daniela KÜhn;Deryk Osthus
Affiliations:
School of mathematics, university of birmingham, edgbaston, birmingham, b15 2tt, uk (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk);School of mathematics, university of birmingham, edgbaston, birmingham, b15 2tt, uk (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
2008

Citing 7
Cited 1

k-linked and k-cyclic digraphs

Journal of Combinatorial Theory Series B
An improved linear edge bound for graph linkages

European Journal of Combinatorics - Special issue: Topological graph theory II
On Sufficient Degree Conditions for a Graph to be $k$-linked

Combinatorics, Probability and Computing
On Minimum Degree Implying That a Graph is H-Linked

SIAM Journal on Discrete Mathematics
Minimum degree conditions for H-linked graphs

Discrete Applied Mathematics
On k-ordered Hamiltonian graphs

Journal of Graph Theory
An extremal problem for H-linked graphs

Journal of Graph Theory

Links in edge-colored graphs

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

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].