Geodesic packing in graphs

Paul Manuel, Boštjan Brešar and Sandi Klavžar

Applied Mathematics and Computation, 2023, vol. 459, issue C

Abstract: A geodesic packing of a graph G is a set of vertex-disjoint maximal geodesics. The maximum cardinality of a geodesic packing is the geodesic packing number gpack(G). It is proved that the decision version of the geodesic packing number is NP-complete. We also consider the geodesic transversal number, gt(G), which is the minimum cardinality of a set of vertices that hit all maximal geodesics in G. While gt(G)≥gpack(G) in every graph G, the quotient gt(G)/gpack(G) is investigated. By using the rook's graph, it is proved that there does not exist a constant C<3 such that gt(G)gpack(G)≤C would hold for all graphs G. If T is a tree, then it is proved that gpack(T)=gt(T), and a linear algorithm for determining gpack(T) is derived. The geodesic packing number is also determined for the strong product of paths.

Keywords: Geodesic packing; Geodesic transversal; Computational complexity; Rook's graph; Diagonal grid (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300323004460
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:459:y:2023:i:c:s0096300323004460

DOI: 10.1016/j.amc.2023.128277

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 ().