Lecture Notes in Computer Science Volume 7034, 2012, pp 75-85

Small Point Sets for Simply-Nested Planar Graphs

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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].