Combinatorial structures on planar maps

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Table of contents

Introduction 
Chapter 1. Combinatorial structures on planar maps 
1. Planar maps
2. The theory of α-orientations
3. Eulerian orientations
4. Bipolar orientations
5. Schnyder woods
6. Transversal structures
Chapter 2. Efficient computation 
1. Computation of α-orientations
2. Computing Eulerian orientations
3. Computing bipolar orientations
4. Computing Schnyder woods
5. Computing transversal structures
6. Appendix: proof of Theorem 2.1
Chapter 3. Bijective counting of maps 
1. Bijections using root-accessible α-orientations
2. Bijections not depending on a root
3. Appendix: proof of Theorem 3.2
Chapter 4. Algorithmic applications 
1. Counting planar maps
2. Coding planar maps
3. Random sampling of planar maps
4. Random sampling of planar graphs
Chapter 5. Straight-line drawing 
1. Drawing using Schnyder woods
2. Drawing using transversal structures
3. Analysis of the drawing algorithms
4. Appendix: proof of Lemma 5.3
Conclusion et perspectives
Bibliography
Index