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A Dirac-Type Result on Hamilton Cycles in Oriented Graphs

Published online by Cambridge University Press:  01 September 2008

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

We show that for each α>0 every sufficiently large oriented graph G with δ+(G), δ−(G)≥3|G|/8+α|G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen [21]. In fact, we prove the stronger result that G is still Hamiltonian if δ(G)+δ+(G)+δ−(G)≥3|G|/2 + α|G|. Up to the term α|G|, this confirms a conjecture of Häggkvist [10]. We also prove an Ore-type theorem for oriented graphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 5 , September 2008 , pp. 689 - 709
Copyright
Copyright © Cambridge University Press 2008

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