AKCE International Journal of Graphs and Combinatorics (Jan 2020)
Strongly connectable digraphs and non-transitive dice
Abstract
We give a new proof of the theorem of Boesch–Tindell and Farzad–Mahdian–Mahmoodian–Saberi–Sadri that a directed graph extends to a strongly connected digraph on the same vertex set if and only if it has no complete directed cut. Our proof bounds the number of edges needed for such an extension; we give examples to demonstrate sharpness. We apply the characterization to a problem on non-transitive dice.
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