Connectivity properties of locally semicomplete digraphs

It is shown that every k ‐connected locally semicomplete digraph D with minimum outdegree at least 2 k and minimum indegree at least 2 k − 2 has at least m = max{2, k } vertices x 1 , x 2 , ⃛, x m such that D − x i is k ‐connected for i = 1, 2, ⃛, m .