A \(k\)-king in a digraph \(D\) is a vertex which can reach every other vertex by a directed path of length at most \(k\). Every tournament with no vertex of in-degree zero has at least three \(2\)-kings. In this paper, we present the structure of tournaments which have exactly three \(2\)-kings and prove that every strong tournament, containing at least \(k+2\) vertices with \(k \geq 3\), has at least \(k+1\) \(k\)-kings.
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