Small Point Sets for Simply-Nested Planar Graphs
Angelini, Patrizio and Di Battista, Giuseppe and Kaufmann, Michael and Mchedlidze, Tamara and Roselli, Vincenzo and Squarcella, Claudio (2012) Small Point Sets for Simply-Nested Planar Graphs. In: Graph Drawing 19th International Symposium, GD 2011, September 21-23, 2011, Eindhoven, The Netherlands , pp. 75-85 (Official URL: http://dx.doi.org/ 10.1007/978-3-642-25878-7_8).
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A point set P ⊆ R2 is universal for a class G if every graph of G has a planar straight-line embedding into P. We prove that there exists a log n O(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.
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