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
Succinct representations of planar maps
Theoretical Computer Science
Generating All Triangulations of Plane Graphs (Extended Abstract)
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
New bijective links on planar maps via orientations
European Journal of Combinatorics
Uniform random sampling of planar graphs in linear time
Random Structures & Algorithms
Progressive lossless mesh compression via incremental parametric refinement
SGP '09 Proceedings of the Symposium on Geometry Processing
A compact encoding of plane triangulations with efficient query supports
Information Processing Letters
Bijections for Baxter families and related objects
Journal of Combinatorial Theory Series A
A bijection for triangulations, quadrangulations, pentagulations, etc.
Journal of Combinatorial Theory Series A
Explicit array-based compact data structures for triangulations
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Unified bijections for maps with prescribed degrees and girth
Journal of Combinatorial Theory Series A
On symmetric quadrangulations and triangulations
European Journal of Combinatorics
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We present a bijection between the set of plane triangulations (aka maximal planar graphs) and a simple subset of the set of plane trees with two leaves adjacent to each node. The construction takes advantage of Schnyder tree decompositions of plane triangulations. This bijection yields an interpretation of the formula for the number of plane triangulations with n vertices. Moreover, the construction is simple enough to induce a linear random sampling algorithm, and an explicit information theory optimal encoding. Finally, we extend our bijection approach to triangulations of a polygon with k sides with m inner vertices, and develop in passing new results about Schnyder tree decompositions for these objects.