2026-07-23T03:49:23Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25160 2026-02-09T08:18:02Z ddc:004 open_access

Geodetic Set on Graphs of Constant Pathwidth and Feedback Vertex Set Number Tale, Prafullkumar Geodetic Sets NP-hardness Constant Treewidth In the Geodetic Set problem, the input consists of a graph G and a positive integer k. The goal is to determine whether there exists a subset S of vertices of size k such that every vertex in the graph is included in a shortest path between two vertices in S. Kellerhals and Koana [IPEC 2020; J. Graph Algorithms Appl 2022] proved that the problem is W[1]-hard when parameterized by the pathwidth or the feedback vertex set number of the input graph. They posed the question of whether the problem admits an XP-algorithm when parameterized by the combination of these two parameters. We answer this in the negative by proving that the problem remains NP-hard even on graphs of constant pathwidth and feedback vertex set number. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Prafullkumar Tale 2025 Is Part Of LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2025.28 urn:nbn:de:0030-drops-251601 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.28 eng https://creativecommons.org/licenses/by/4.0/legalcode