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

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-30 DOI:10.1016/j.disc.2024.114297

Nicolas Bousquet , Quentin Chuet , Victor Falgas–Ravry , Amaury Jacques , Laure Morelle

引用次数: 0

Abstract

In this short note, we prove that every twin-free graph on n vertices contains a locating-dominating set of size at most

⌈ \frac{5}{8} n ⌉

. This improves the earlier bound of

⌊ \frac{2}{3} n ⌋

due to Foucaud, Henning, Löwenstein and Sasse from 2016, and makes some progress towards the well-studied locating-dominating conjecture of Garijo, González and Márquez.

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关于无孪生图中定位支配集的说明

在这篇短文中，我们证明了 n 个顶点上的每个无孪生图都包含一个大小至多为⌈58n⌉的定位支配集。这改进了 Foucaud、Henning、Löwenstein 和 Sasse 在 2016 年提出的⌊23n⌋ 的早期约束，并在实现 Garijo、González 和 Márquez 的定位支配猜想方面取得了一些进展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.