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Abstract
We show that for each alpha > 0 every sufficiently large oriented graph G with delta(+)(G),delta()(G) >= 3\G\/8 + alpha\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 delta(G) + delta(+)(G) + delta()(G) >= 3\G\/2 + alpha\G\. Up to the term alpha\G\, this confirms a conjecture of Haggkvist [10]. We also prove an Oretype theorem for oriented graphs.
Original language  English 

Journal  Combinatorics, Probability and Computing 
Volume  17 
Issue number  05 
Early online date  4 Jul 2008 
DOIs  
Publication status  Published  1 Sept 2008 
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Dive into the research topics of 'A DiracType Result on Hamilton Cycles in Oriented Graphs'. Together they form a unique fingerprint.Projects
 2 Finished

Directed graphs and the regularity method
Kuhn, D. (Principal Investigator) & Osthus, D. (CoInvestigator)
Engineering & Physical Science Research Council
1/10/07 → 31/03/11
Project: Research Councils

Graph expansion and applications
Osthus, D. (Principal Investigator)
Engineering & Physical Science Research Council
1/08/07 → 30/11/09
Project: Research Councils