**Conjecture**Every simple eulerian graph on vertices can be decomposed into at most cycles.

This conjecture is tight because a complete graph on vertices cannot be covered by less than cycles.

There is a similar conjecture about decomposition of a connected graph into paths.

## Bibliography

* [L] L. Lovász, On covering of graphs. In Theory of Graphs (Proc. Colloq., Tihany, 1966), 231--236. Academic Press, New York, 1968.

* indicates original appearance(s) of problem.