Complexity of metric dimension on planar graphs

@article{Daz2017ComplexityOM,
  title={Complexity of metric dimension on planar graphs},
  author={J. D{\'i}az and O. Pottonen and M. Serna and E. J. V. Leeuwen},
  journal={J. Comput. Syst. Sci.},
  year={2017},
  volume={83},
  pages={132-158}
}
Abstract The metric dimension of a graph G is the size of a smallest subset L ⊆ V ( G ) such that for any x , y ∈ V ( G ) with x ≠ y there is a z ∈ L such that the graph distance between x and z differs from the graph distance between y and z. Even though this notion has been part of the literature for almost 40 years, prior to our work the computational complexity of determining the metric dimension of a graph was still very unclear. In this paper, we show tight complexity boundaries for the… Expand
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