It is shown that there exists a positive ε so that for any integer k, every directed graph with minimum outdegree at least k contains at least εk vertex disjoint cycles. On the other hand, for every k there is a digraph with minimum outdegree k which does not contain two vertex or edge disjoint cycles of the same length.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics