Small sets supporting fary embeddings of planar graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Area requirement and symmetry display of planar upward drawings
Discrete & Computational Geometry
A note on optimal area algorithms for upward drawings of binary trees
Computational Geometry: Theory and Applications
Area-efficient upward tree drawings
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
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
Grid Embedding of 4-Connected Plane Graphs
GD '95 Proceedings of the Symposium on Graph Drawing
Drawing planar graphs using the lmc-ordering
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Efficient Generation of Plane Triangulations without Repetitions
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Convex Grid Drwaings of Four-Connected Plane Graphs
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
A Lower Bound on the Area Requirements of Series-Parallel Graphs
Graph-Theoretic Concepts in Computer Science
A note on minimum-area straight-line drawings of planar graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
GD'09 Proceedings of the 17th international conference on Graph Drawing
Small point sets for simply-nested planar graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
Universal line-sets for drawing planar 3-trees
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Grid drawings and the chromatic number
GD'12 Proceedings of the 20th international conference on Graph Drawing
Reprint of: Grid representations and the chromatic number
Computational Geometry: Theory and Applications
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Given a plane graph G, we wish to draw it in the plane in such a way that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints. An additional objective is to minimize the size of the resulting grid. It is known that each plane graph can be drawn in such a way in an (n - 2) x (n - 2) grid (for n = 3), and that no grid smaller than (2n3 - 1) x (2n3 - 1) can be used for this purpose, if n is a multiple of 3. In fact, for all n = 3, each dimension of the resulting grid needs to be at least @?2(n - 1)3@?, even if the other one is allowed to be unbounded. In this paper we show that this bound is tight by presenting a grid drawing algorithm that produces drawings of width @?2(n - 1)3@?. The height of the produced drawings is bounded by 4@?2(n - 1)3@? - 1. Our algorithm runs in linear time and is easy to implement.