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The Metric Dimension problem asks for a minimum-sized resolving set in agiven (unweighted, undirected) graph $G$. Here, a set $S \subseteq V(G)$ isresolving if no two distinct vertices of $G$ have the same distance vector to$S$. The complexity of Metric Dimension in graphs of bounded treewidth remainedelusive in the past years. Recently, Bonnet and Purohit [IPEC 2019] showed thatthe problem is W[1]-hard under treewidth parameterization. In this work, westrengthen their lower bound to show that Metric Dimension is NP-hard in graphsof treewidth 24.

Hardness of Metric Dimension in Graphs of Constant Treewidth