A note on locating-dominating sets in twin-free graphs

TL;DR

This paper proves that twin-free graphs have a locating-dominating set of size at most 5/8 of the vertices, improving previous bounds and advancing the understanding of the locating-dominating problem.

Contribution

It establishes a tighter upper bound for locating-dominating sets in twin-free graphs, improving upon earlier results and contributing to the conjecture in the field.

Findings

Upper bound of 5/8 n for twin-free graphs

Improvement over previous 2/3 n bound

Progress towards the locating-dominating conjecture

Abstract

In this short note, we prove that every twin-free graph on $n$ vertices contains a locating-dominating set of size at most $\lceil\frac{5}{8}n\rceil$. This improves the earlier bound of $\lfloor\frac{2}{3}n\rfloor$ due to Foucaud, Henning, L\"owenstein and Sasse from 2016, and makes some progress towards the well-studied locating-dominating conjecture of Garijo, Gonz\'alez and M\'arquez.