A lower bound on the size of universal sets for planar graphs
ACM SIGACT News
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
A 1.235 lower bound on the number of points needed to draw all n-vertex planar graphs
Information Processing Letters
Curve-constrained drawings of planar graphs
Computational Geometry: Theory and Applications
On simultaneous planar graph embeddings
Computational Geometry: Theory and Applications
Universal Sets of n Points for One-bend Drawings of Planar Graphs with n Vertices
Discrete & Computational Geometry
Universal line-sets for drawing planar 3-trees
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Point-Set embeddability of 2-colored trees
GD'12 Proceedings of the 20th international conference on Graph Drawing
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A universal point-set supports a crossing-free drawing of any planar graph. For a planar graph with n vertices, if bends on edges of the drawing are permitted, universal point-sets of size n are known, but only if the bend-points are in arbitrary positions. If the locations of the bend-points must also be specified as part of the point-set, we prove that any planar graph with n vertices can be drawn on a universal set $\cal S$ of O(n2/logn) points with at most one bend per edge and with the vertices and the bend points in $\cal S$ . If two bends per edge are allowed, we show that O(nlogn) points are sufficient, and if three bends per edge are allowed, Θ(n) points are sufficient. When no bends on edges are permitted, no universal point-set of size o(n2) is known for the class of planar graphs. We show that a set of n points in balanced biconvex position supports the class of maximum degree 3 series-parallel lattices.