2023/03/19 by Nicolás Bousquet, Quentin Deschamps, Bousquet, Nicolas +3
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2303.10646
openalex publication_date 2023/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The metric dimension has been introduced independently by Harary, Melter and Slater in 1975 to identify vertices of a graph G using its distances to a subset of vertices of G. A resolving set X of a graph G is a subset of vertices such that, for every pair (u,v) of vertices of G, there is a vertex x in X such that the distance between x and u and the distance between x and v are distinct. The metric dimension of the graph is the minimum size of a resolving set. Computing the metric dimension of a graph is NP-hard even on split graphs and interval graphs. Bonnet and Purohit proved that the metric dimension problem is W[1]-hard parameterized by treewidth. Li and Pilipczuk strenghtened this result by showing that it is NP-hard for graphs of treewidth. In this article, we prove that that metric dimension is FPT parameterized by treewidth in chordal graphs.