Complexity of metric dimension on planar graphs
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hdl:2117/114459
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Data publicació2017-04-03
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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 Metric Dimension problem. We achieve this by giving two complementary results. First, we show that the Metric Dimension problem on planar graphs of maximum degree 6 is NP-complete. Then, we give a polynomial-time algorithm for determining the metric dimension of outerplanar graphs.
Descripció
© <year>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
CitacióDiaz, J., Pottonen, O., Serna, M., van Leeuwen, E.J. Complexity of metric dimension on planar graphs. "Journal of computer and system sciences", 3 Abril 2017, vol. 83, núm. 1, p. 132-158.
ISSN0022-0000
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