 
Summary: EdgeDisjoint Cycles in Regular Directed Graphs
Noga Alon
Colin McDiarmid
Michael Molloy
February 22, 2002
Abstract
We prove that any kregular directed graph with no parallel edges
contains a collection of at least (k2
) edgedisjoint cycles, conjecture that
in fact any such graph contains a collection of at least k+1
2
disjoint cycles,
and note that this holds for k 3.
In this paper we consider the maximum size of a collection of edgedisjoint
cycles in a directed graph. We pose the following conjecture:
Conjecture 1: If G is a kregular directed graph with no parallel edges,
then G contains a collection of k+1
2 edgedisjoint cycles.
We prove two weaker results:
Theorem 1: If G is a kregular directed graph with no parallel edges, then
