New bijective links on planar maps via orientations

A Generic Method for Bijections between Blossoming Trees and Planar Maps

This article presents a unified bijective scheme between planar maps and blossoming trees, where a blossoming tree is defined as a spanning tree of the map decorated with some dangling half-edges that enable to reconstruct its faces. Our method generalizes a previous construction of Bernardi by loosening its conditions of application so as to include annular maps, that is maps embedded in the p...

New bijective links on planar maps

This article describes new bijective links on planar maps, which are of incremental complexity and present original features. The first two bijections Φ1,2 are correspondences on oriented planar maps. They can be considered as variations on the classical edge-poset construction for bipolar orientations on graphs, suitably adapted so as to operate only on the embeddings in a simple local way. In...

A unified bijective method for maps: application to two classes with boundaries

Based on a construction of the first author, we present a general bijection between certain decorated plane trees and certain orientations of planar maps with no counterclockwise circuit. Many natural classes of maps (e.g. Eulerian maps, simple triangulations,...) are in bijection with a subset of these orientations, and our construction restricts in a simple way on the subset. This gives a gen...

Lix, ´ Ecole Polytechnique Et Projet Algo, Inria Rocquencourt Combinatoire Des Cartes Planaires Et Applications Algorithmiques

This thesis describes algorithms on planar maps (graphs embedded in the plane without edge-crossings) based on their combinatorial properties. For several important families of planar maps (3-connected, triangulations, quadrangulations), efficient procedures of random generation, encoding, and straight-line drawing are described. In particular, the first optimal encoder for the combinatorial in...

Multiplicative bijective maps on standard operator algebras