A Dirac-Type Result on Hamilton Cycles in Oriented Graphs

@article{Kelly2007ADR,
  title={A Dirac-Type Result on Hamilton Cycles in Oriented Graphs},
  author={Luke Kelly and Daniela K{\"u}hn and Deryk Osthus},
  journal={Combinatorics, Probability & Computing},
  year={2007},
  volume={17},
  pages={689-709}
}
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 Haggkvist [10]. We also prove an Ore-type theorem for oriented graphs. 

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