On the optimality of 3-restricted arc connectivity for digraphs and bipartite digraphs

Abstract

Let D be a strong digraph. An arc subset S is a k-restricted arc cut of D if D − S has a strong component D ′ with order at least k such that D\V (D ′) contains a connected subdigraph with order at least k. If such a k-restricted arc cut exists in D, then D is called λ k-connected. For a λ kconnected digraph D, the k-restricted arc connectivity, denoted by λ k (D), is the minimum cardinality over all k-restricted arc cuts of D. It is known that for many digraphs λ k (D) ≤ ξ k (D), where ξ k (D) denotes the minimum k-degree of D. D is called λ k-optimal if λ k (D) = ξ k (D). In this paper, we will give some sufficient conditions for digraphs and bipartite digraphs to be λ 3-optimal.