Small sets supporting fary embeddings of planar graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Dynamic Graph Drawings: Trees, Series-Parallel Digraphs, and Planar ST-Digraphs
SIAM Journal on Computing
A better heuristic for orthogonal graph drawings
Computational Geometry: Theory and Applications
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Characterizing bar line-of-sight graphs
SCG '85 Proceedings of the first annual symposium on Computational geometry
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Drawing Algorithms for Series-Parallel Digraphs in Two and Three Dimensions
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Drawing Outer-Planar Graphs in O(n log n) Area
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Layout of Graphs with Bounded Tree-Width
SIAM Journal on Computing
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
On the Parameterized Complexity of Layered Graph Drawing
Algorithmica - Parameterized and Exact Algorithms
A Lower Bound on the Area Requirements of Series-Parallel Graphs
Graph-Theoretic Concepts in Computer Science
On the two-dimensional orthogonal drawing of series-parallel graphs
Discrete Applied Mathematics
Small area drawings of outerplanar graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Improved lower bounds on the area requirements of series-parallel graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Small grid drawings of planar graphs with balanced bipartition
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Small grid drawings of planar graphs with balanced partition
Journal of Combinatorial Optimization
h-quasi planar drawings of bounded treewidth graphs in linear area
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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In this paper, we study small planar drawings of planar graphs. For arbitrary planar graphs, Θ(n2) is the established upper and lower bound on the worst-case area. It is a long-standing open problem for what graphs smaller area can be achieved, with results known only for trees and outer-planar graphs. We show here that series-parallel can be drawn in O(n3/2) area, but 2-outer-planar graphs and planar graphs of proper pathwidth 3 require Ω(n2) area.