The main results of this thesis are the following. We show that for each α > 0 every sufficiently large oriented graph G with minimum indegree and minimum outdegree at least 3|G|/8 + α|G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen. Furthermore, answering completely a conjecture of Häggkvist and Thomason, we show that we get every possible orientation...

Tewes and Volkmann [Australas. J. Combin. 18 (1998), 293–301] proved that for an integer k ≥ 3, every in-tournament of minimum in-degree d ≥ 1 and of order at most kd contains a directed cycle of length at most k. In other words, they proved that the Caccetta-Häggkvist conjecture, with respect to the minimum in-degree, is true for in-tournaments. In the same paper, they proved also that every s...

The balanced hypercube BHn is a variant of the hypercube Qn. Huang and Wu proved that BHn has better properties than Qn with the same number of links and processors. In particularly, they showed that there exists a cycle of length 2 l in BHn for all l, 2 6 l 6 2n. In this paper, we improve this result by showing that BHn is edge-pancyclic, which means that for arbitrary edge e, there exists a c...