Strongly connectable digraphs and non-transitive dice
Combinatorics
2021-06-16 v3
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.
Keywords
Cite
@article{arxiv.1508.00313,
title = {Strongly connectable digraphs and non-transitive dice},
author = {Simon Joyce and Alex Schaefer and Douglas B. West and Thomas Zaslavsky},
journal= {arXiv preprint arXiv:1508.00313},
year = {2021}
}
Comments
8 pp. V2: 9 pp. Cite previous publication of one theorem. V3: Minor copyedits