Geodesic
Arbitrary orientations of Hamilton cycles in oriented graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We use a randomised embedding method to prove that for all $\alpha>0$ any sufficiently large oriented graph $G$ with minimum in-degree and out-degree $\delta^+(G),\delta^-(G)\geq (3/8+\alpha)|G|$ contains every possible orientation of a Hamilton cycle. This confirms a conjecture of Häggkvist and Thomason.
DOI : 10.37236/673
Classification : 05C45, 05C20, 05C38, 05C40
Mots-clés : randomized embedding method, oriented graph, orientation, Hamilton cycle 
@article{10_37236_673,
     author = {Luke Kelly},
     title = {Arbitrary orientations of {Hamilton} cycles in oriented graphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/673},
     zbl = {1236.05120},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/673/}
}
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Luke Kelly. Arbitrary orientations of Hamilton cycles in oriented graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/673

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