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 λk-connected. For a λk-connected digraph D, the k-restricted arc connectivity, denoted by λk(D), is the minimum cardinality over all k-restricted arc cuts of D. It is known that for many digraphs λk(D) ≤ ξk(D), where ξk(D) denotes the minimum k-degree of D. D is called λk-optimal if λk(D) = ξk(D). In this paper, we will give some sufficient conditions for digraphs and bipartite digraphs to be λ3-optimal.

Keywords

• restricted arc-connectivity
• bipartite digraph
• optimality
• digraph
• network
• 05c40
• 68r10