Let D=(V,E) be a minimally k-edge-connected simple directed graph. We prove that there is a function f(k) such that |V|≥f(k) implies |E|≤2k(|V|-k). We also determine the extremal graphs whose size attains this upper bound.
- Directed graphs
- Minimally k-edge-connected
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics