Locating Dominating Sets in local tournaments
Thomas Bellitto, Caroline Brosse, Benjamin L\'ev\^eque, Aline Parreau

TL;DR
This paper extends bounds on the size of locating dominating sets in special classes of directed graphs, including local tournaments and quasi-twin-free digraphs, improving understanding of their structural properties.
Contribution
It generalizes known bounds for tournaments to connected local tournaments and quasi-twin-free digraphs with a supervising vertex.
Findings
Bound of rac{2n}{3} for connected local tournaments.
Bound of rac{2n}{3} for quasi-twin-free digraphs with a supervising vertex.
Improves previous bounds for specific classes of directed graphs.
Abstract
A dominating set in a directed graph is a set of vertices such that all the vertices that do not belong to have an in-neighbour in . A locating set is a set of vertices such that all the vertices that do not belong to are characterized uniquely by the in-neighbours they have in , i.e. for every two vertices and that are not in , there exists a vertex that dominates exactly one of them. The size of a smallest set of a directed graph which is both locating and dominating is denoted by . Foucaud, Heydarshahi and Parreau proved that any twin-free digraph satisfies but conjectured that this bound can be lowered to . The conjecture is still open. They also proved that if is a tournament, i.e. a directed graph where there is one arc between every pair of vertices, then…
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory
