A1 Refereed original research article in a scientific journal

Progress towards the two-thirds conjecture on locating-total dominating sets




AuthorsChakraborty, Dipayan; Foucaud, Florent; Hakanen, Anni; Henning, Michael A.; Wagler, Annegret K.

PublisherElsevier

Publication year2024

JournalDiscrete Mathematics

Journal name in sourceDiscrete Mathematics

Article number114176

Volume347

Issue12

ISSN0012-365X

eISSN1872-681X

DOIhttps://doi.org/10.1016/j.disc.2024.114176(external)

Web address https://doi.org/10.1016/j.disc.2024.114176(external)

Self-archived copy’s web addresshttps://research.utu.fi/converis/portal/detail/Publication/457313437(external)

Preprint addresshttps://arxiv.org/abs/2211.14178(external)


Abstract
We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set S of vertices of a graph G is a locating-total dominating set if every vertex of G has a neighbor in S, and if any two vertices outside S have distinct neighborhoods within S. The smallest size of such a set is denoted by γtL(G). It has been conjectured that γtL(G)≤2n3 holds for every twin-free graph G of order n without isolated vertices. We prove that the conjecture holds for cobipartite graphs, split graphs, block graphs and subcubic graphs.



Last updated on 2025-27-01 at 19:02