Adding and Reversing Arcs in Semicomplete Digraphs

Authors:
Jørgen Bang-Jensen;Tibor Jordán
Affiliations:
Department of Mathematics and Computer Science, Odense University, Campusvej 55 DK-5230 Odense, Denmark (e-mail: jbj@imada.ou.dk and tibor@imada.ou.dk);Department of Mathematics and Computer Science, Odense University, Campusvej 55 DK-5230 Odense, Denmark (e-mail: jbj@imada.ou.dk and tibor@imada.ou.dk)
Venue:
Combinatorics, Probability and Computing
Year:
1998

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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≥3k−1, then ak(T)=rk(T). We also show that this bound on n is best possible.