Abstract
A point set P ⊆ ℝ2 is universal for a class \(\cal G\) if every graph of \({\cal G}\) has a planar straight-line embedding into P. We prove that there exists a \(O(n (\frac{\log n}{\log\log n})^2)\) size universal point set for the class of simply-nested n-vertex planar graphs. This is a step towards a full answer for the well-known open problem on the size of the smallest universal point sets for planar graphs [1, 5, 9].
Research partially supported by the MIUR project AlgoDEEP prot. 2008TFBWL4, by the ESF project 10-EuroGIGA-OP-003 GraDR “Graph Drawings and Representations”, and by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: Heracleitus II. Investing in knowledge society through the European Social Fund.
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Angelini, P., Di Battista, G., Kaufmann, M., Mchedlidze, T., Roselli, V., Squarcella, C. (2012). Small Point Sets for Simply-Nested Planar Graphs. In: van Kreveld, M., Speckmann, B. (eds) Graph Drawing. GD 2011. Lecture Notes in Computer Science, vol 7034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25878-7_8
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DOI: https://doi.org/10.1007/978-3-642-25878-7_8
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