A dirac-type result on hamilton cycles in oriented graphs

  • Authors:

  • Luke Kelly;Daniela KÜhn;Deryk Osthus

  • Affiliations:

  • 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);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);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)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2008

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Abstract

We show that for each α0 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.