It is shown that every k-connected locally semicomplete digraph D with
minimum outdegree at least 2k and minimum indegree at least 2k - 2 ha
s at least m = max{2, k} vertices x1, x2, . . ., x(m) such that D - x(
i) is k-connected for i = 1, 2, ..., m. (C) 1994 John Wiley & Sons, In
c.