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Edge-Disjoint Cycles in Regular Directed Graphs Colin McDiarmid
 

Summary: Edge-Disjoint Cycles in Regular Directed Graphs
Noga Alon
Colin McDiarmid
Michael Molloy
February 22, 2002
Abstract
We prove that any k-regular directed graph with no parallel edges
contains a collection of at least (k2
) edge-disjoint 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 edge-disjoint
cycles in a directed graph. We pose the following conjecture:
Conjecture 1: If G is a k-regular directed graph with no parallel edges,
then G contains a collection of k+1
2 edge-disjoint cycles.
We prove two weaker results:
Theorem 1: If G is a k-regular directed graph with no parallel edges, then

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics