Small sets supporting fary embeddings of planar graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A lower bound on the size of universal sets for planar graphs
ACM SIGACT News
A linear-time algorithm for drawing a planar graph on a grid
Information Processing Letters
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Minimum-Width Grid Drawings of Plane Graphs
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Upward Straight-Line Embeddings of Directed Graphs into Point Sets
Graph-Theoretic Concepts in Computer Science
Upward straight-line embeddings of directed graphs into point sets
Computational Geometry: Theory and Applications
Universal sets of n points for 1-bend drawings of planar graphs with n vertices
GD'07 Proceedings of the 15th international conference on Graph drawing
The hamiltonian augmentation problem and its applications to graph drawing
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Orthogeodesic point-set embedding of trees
GD'11 Proceedings of the 19th international conference on Graph Drawing
On point-sets that support planar graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
Small point sets for simply-nested planar graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
On point-sets that support planar graphs
Computational Geometry: Theory and Applications
Point-Set embeddability of 2-colored trees
GD'12 Proceedings of the 20th international conference on Graph Drawing
Universal point sets for planar three-trees
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We study a problem of lower bounds on straight line drawings of planar graphs. We show that at least 1.235 ċ n points in the plane are required to draw each n-vertex planar graph with edges drawn as straight line segments (for sufficiently large n). This improves the previous best bound of 1.206 ċ n (for sufficiently large n) due to Chrobak and Karloff [Sigact News 20 (4) (1989) 83-86]. Our contribution is twofold: we improve the lower bound itself and we give a significantly simpler and more straightforward proof.