A note on some embedding problems for oriented graphs

Details A note on some embedding problems for oriented graphs A note on some embedding problems for oriented graphs

2010-11-19

arxiv.org/abs/1011.4476v1

Mathematics

Combinatorics

6 pages, 2 figures

Scientific paper

We conjecture that every oriented graph $G$ on $n$ vertices with $\delta ^+
(G) , \delta ^- (G) \geq 5n/12$ contains the square of a Hamilton cycle. We
also give a conjectural bound on the minimum semidegree which ensures a perfect
packing of transitive triangles in an oriented graph. A link between Ramsey
numbers and perfect packings of transitive tournaments is also considered.

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