The geodesic-transversal problem

Paul Manuel, Boštjan Brešar and Sandi Klavžar

Applied Mathematics and Computation, 2022, vol. 413, issue C

Abstract: A maximal geodesic in a graph is a geodesic (alias shortest path) which is not a subpath of a longer geodesic. The geodesic-transversal problem in a graph G is introduced as the task to find a smallest set S of vertices of G such that each maximal geodesic has at least one vertex in S. The minimum cardinality of such a set is the geodesic-transversal number gt(G) of G. It is proved that gt(G)=1 if and only if G is a subdivided star and that the geodesic-transversal problem is NP-complete. Fast algorithms to determine the geodesic-transversal number of trees and of spread cactus graphs are designed, respectively.

Keywords: Hitting set; Geodesic-transversal problem; Network centrality; Tree; Cactus graph; Algorithm (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300321007050
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:413:y:2022:i:c:s0096300321007050

DOI: 10.1016/j.amc.2021.126621

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 ().