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The geodesic-transversal problem

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  • Manuel, Paul
  • Brešar, Boštjan
  • Klavžar, Sandi

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.

Suggested Citation

  • Manuel, Paul & Brešar, Boštjan & Klavžar, Sandi, 2022. "The geodesic-transversal problem," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    • Handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321007050
    DOI: 10.1016/j.amc.2021.126621
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    References listed on IDEAS

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    4. Iztok Peterin & Gabriel Semanišin, 2021. "On the Maximal Shortest Paths Cover Number," Mathematics, MDPI, vol. 9(14), pages 1-10, July.
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    Cited by:

    1. Manuel, Paul & Brešar, Boštjan & Klavžar, Sandi, 2023. "Geodesic packing in graphs," Applied Mathematics and Computation, Elsevier, vol. 459(C).

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