On the Optimality of 3-Restricted Arc Connectivity for Digraphs and Bipartite Digraphs

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^k-connected 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 λ³-optimal.