3-Restricted arc connectivity of digraphs

Let D be a strong digraph with order n≥6 and minimum degree δ(D). In this paper, we first show that λ3(D) exists if δ(D)≥3 and, furthermore, λ3(D)≤ξ3(D) if δ(D)≥4, where ξ3(D) is the minimum 3-degree of D. Next, we prove that λ3(D)=ξ3(D) if δ(D)≥n+32. Finally, we give examples showing that these results are best possible in some sense.