Directed cycle [formula omitted]-connectivity of complete digraphs and complete regular bipartite digraphs.

Let D = (V , A) be a digraph of order n , S a subset of V of size k , where k is a positive integer and 2 ≤ k ≤ n. A directed cycle C of D is called a directed S -Steiner cycle (or, an S -cycle for short) if S ⊆ V (C). Steiner cycles have applications in the optimal design of reliable telecommunication and transportation networks. A pair of S -cycles is called internally disjoint if they have no common arc and the common vertex set of them is exactly S. Let κ S c (D) be the maximum number of pairwise internally disjoint S -cycles in D. The directed cycle k -connectivity of D is defined as κ k c (D) = min κ S c (D) ∣ S ⊆ V (D) , S = k , 2 ≤ k ≤ n. In this paper, we study the directed cycle k -connectivity of complete digraphs K ↔ n and complete regular bipartite digraphs K ↔ a , a. We give a sharp lower bound for κ k c ( K ↔ n) and determine the exact values for κ k c ( K ↔ n) when k ∈ { 2 , 3 , 4 , 6 }. We also determine the exact value of κ k c ( K ↔ a , a) for each 2 ≤ k ≤ n. [ABSTRACT FROM AUTHOR]