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research
Complexity of metric dimension on planar graphs
Authors
Josep Díaz Cort
Ollie Pottonen
María José Serna Iglesias
Erik Jan van Leeuwen
Publication date
12 July 2016
Publisher
'Elsevier BV'
Doi
Cite
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on
arXiv
Abstract
© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/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.Peer ReviewedPostprint (author's final draft
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