Decomposing an eulerian graph into cycles.

Importance: Medium ✭✭
Author(s): Hajós, G.
Recomm. for undergrads: no
Posted by: fhavet
on: March 4th, 2013
Conjecture   Every simple eulerian graph on $ n $ vertices can be decomposed into at most $ \frac{1}{2}(n-1) $ cycles.

This conjecture is tight because a complete graph on $ 2k+1 $ vertices cannot be covered by less than $ k $ cycles.

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


* [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.