Adding and Reversing Arcs in Semicomplete Digraphs

Abstract

Let T be a semicomplete digraph on n vertices. Let ak(T) denote the minimum number of arcs whose addition to T results in a k-connected semicomplete digraph and let rk(T) denote the minimum number of arcs whose reversal in T results in a k-connected semicomplete digraph. We prove that if n[ges ]3k−1, then ak(T)=rk(T). We also show that this bound on n is best possible.