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Minimally $$k$$-edge-connected directed graphs of maximal size. (English) Zbl 1062.05079
Summary: Let $$D=(V,E)$$ be a minimally $$k$$-edge-connected simple directed graph. We prove that there is a function $$f(k)$$ such that $$|V| \geq f(k)$$ implies $$|E| \leq 2k(|V|-k)$$. We also determine the extremal graphs whose size attains this upper bound.

##### MSC:
 05C40 Connectivity 05C35 Extremal problems in graph theory
##### Keywords:
Directed graphs; Edge-connectivity
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