Abstract
We survey results and possible results of the following type: given positive integers n , k , d , is there an integer h d ( n , k ) so that every n-connected, finite graph (digraph) G of order at least h d ( n , k ) contains a set W of exactly k vertices so that G - W is ( n - d ) -connected? For digraphs, these question have not really been studied before, so almost all problems are open.
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