On finding the rectangular duals of planar triangular graphs
SIAM Journal on Computing
Bipolar orientations revisited
Discrete Applied Mathematics - Special issue: Fifth Franco-Japanese Days, Kyoto, October 1992
Planarity and edge poset dimension
European Journal of Combinatorics
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
A bijective census of nonseparable planar maps
Journal of Combinatorial Theory Series A
Random maps, coalescing saddles, singularity analysis, and airy phenomena
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Combinatorial Enumeration
Optimal Coding and Sampling of Triangulations
Algorithmica
Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling
ACM Transactions on Algorithms (TALG)
Bijective counting of plane bipolar orientations and Schnyder woods
European Journal of Combinatorics
| Hi-index | 0.00 |
This article presents new bijections on planar maps. At first a bijection is established between bipolar orientations on planar maps and specific ''transversal structures'' on triangulations of the 4-gon with no separating 3-cycle, which are called irreducible triangulations. This bijection specializes to a bijection between rooted non-separable maps and rooted irreducible triangulations. This yields in turn a bijection between rooted loopless maps and rooted triangulations, based on the observation that loopless maps and triangulations are decomposed in a similar way into components that are respectively non-separable maps and irreducible triangulations. This gives another bijective proof (after Wormald's construction published in 1980) of the fact that rooted loopless maps with n edges are equinumerous to rooted triangulations with n inner vertices.