# Long directed cycles in diregular digraphs

**Conjecture**Every strong oriented graph in which each vertex has indegree and outdegree at least contains a directed cycle of length at least .

The disjoint union of two regular tournaments on vertices shows that this would be best possible.

If the oriented graph has order at most , Jackson conjecture the existence of a longer cycle, namely a Hamilton cycle

## Bibliography

*[J] B. Jackson. Long paths and cycles in oriented graphs. J. Graph Theory 5 (1981), 145--157.

* indicates original appearance(s) of problem.