A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
Embedding planar graphs in four pages
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Efficient message routing in planar networks
SIAM Journal on Computing
Generating triangulations at random
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Short encodings of planar graphs and maps
Discrete Applied Mathematics
Random sampling of large planar maps and convex polyhedra
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Random generation of trees and other combinatorial objects
Theoretical Computer Science - Special issue on Caen '97
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
A Fast General Methodology for Information-Theoretically Optimal Encodings of Graphs
SIAM Journal on Computing
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Near-optimal connectivity encoding of 2-manifold polygon meshes
Graphical Models - Special issue: Processing on large polygonal meshes
Compact Routing Tables for Graphs of Bounded Genus
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Planar Maps and Airy Phenomena
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Compact Oracles for Reachability and Approximate Distances in Planar Digraphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Extremal Graph Theory
Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Journal of Combinatorial Theory Series B
Dissections and trees, with applications to optimal mesh encoding and to random sampling
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Random planar graphs with n nodes and a fixed number of edges
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Generating labeled planar graphs uniformly at random
Theoretical Computer Science
The random planar graph process
Random Structures & Algorithms
Generating unlabeled connected cubic planar graphs uniformly at random
Random Structures & Algorithms
Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling
ACM Transactions on Algorithms (TALG)
Schnyder woods for higher genus triangulated surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Quick encoding of plane graphs in log 214 bits per edge
Information Processing Letters
Optimal coding and sampling of triangulations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Generating labeled planar graphs uniformly at random
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A compact encoding of plane triangulations with efficient query supports
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
A compact encoding of plane triangulations with efficient query supports
Information Processing Letters
An application of well-orderly trees in graph drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Sampling unlabeled biconnected planar graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Nearly optimal visibility representations of plane graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Planar graphs, via well-orderly maps and trees
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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We propose a new linear time algorithm to represent a planar graph. Based on a specific triangulation of the graph, our coding takes on average 5.03 bits per node, and 3.37 bits per node if the graph is maximal. We derive from this representation that the number of unlabeled planar graphs with n nodes is at most 2驴n+O(log n), where 驴 驴 5.007. The current lower bound is 2脽n+驴(log n) for 脽 驴 4.71. We also show that almost all unlabeled and almost all labeled n-node planar graphs have at least 1.70n edges and at most 2.54n edges.