Domination of triangulated discs and maximal outerplanar graphs

Jarne Renders, Shin-ichi Tokunaga and Carol T. Zamfirescu

Applied Mathematics and Computation, 2024, vol. 473, issue C

Abstract: Given an infinite family of graphs, its domination ratio is the smallest real k such that for every large enough graph in the family, the ratio between its domination number and order is at most k. We give bounds for the domination ratios of various families of triangulated discs, disproving two conjectures of Tokunaga. For instance, we show that the domination ratio of triangulated discs of minimum degree 3 is at least 3/10. We also give a natural extension of a theorem on the domination number of maximal outerplane graphs, proven by Campos and Wakabayashi, and independently Tokunaga. Motivated by the Matheson-Tarjan Conjecture, we present observations on dominating triangulations via Jackson-Yu decomposition trees as well as an approach on how to efficiently dominate, given a triangulation, many large subtriangulations thereof. Throughout the paper, results are accompanied by computational experiments.

Keywords: Domination number; Outerplanar graph; Triangulation (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324001206
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:473:y:2024:i:c:s0096300324001206

DOI: 10.1016/j.amc.2024.128648

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().