Planar Graphs, via Well-Orderly Maps and Trees

@article{Bonichon2006PlanarGV,
  title={Planar Graphs, via Well-Orderly Maps and Trees},
  author={N. Bonichon and C. Gavoille and N. Hanusse and Dominique Poulalhon and G. Schaeffer},
  journal={Graphs and Combinatorics},
  year={2006},
  volume={22},
  pages={185-202}
}
The family of well-orderly maps is a family of planar maps with the property that every connected planar graph has at least one plane embedding which is a well-orderly map. We show that the number of well-orderly maps with n nodes is at most 2αn+O(logn), where α≈4.91. A direct consequence of this is a new upper bound on the number p(n) of unlabeled planar graphs with n nodes, log2p(n)≤4.91n.The result is then used to show that asymptotically almost all (labeled or unlabeled), (connected or not… Expand
21 Citations
The Degree Distribution of Random Planar Graphs
  • 1
  • Highly Influenced
  • PDF
Fast and compact planar embeddings
Lower bounds for protrusion replacement by counting equivalence classes
  • 1
  • PDF
Fast and Compact Planar Embeddings
  • 11
  • PDF
Random Graphs, Geometry and Asymptotic Structure
  • 8
A Census of Plane Graphs with Polyline Edges
  • 4
  • PDF
Feynman diagrams and rooted maps
  • 11
  • PDF
...
1
2
3
...

References

SHOWING 1-10 OF 36 REFERENCES
Optimal Coding and Sampling of Triangulations
  • 132
  • PDF
A bijection between realizers of maximal plane graphs and pairs of non-crossing Dyck paths
  • N. Bonichon
  • Computer Science, Mathematics
  • Discret. Math.
  • 2005
  • 51
Random planar graphs
  • 142
  • PDF
Received: October 1, 2004 Final version received
  • Received: October 1, 2004 Final version received
  • 2005
Combinatorial Enumeration
  • 678
Compact oracles for reachability and approximate distances in planar digraphs
  • M. Thorup
  • Mathematics, Computer Science
  • JACM
  • 2004
  • 258
On the Number of Edges in Random Planar Graphs
  • 47
...
1
2
3
4
...