A bijection between realizers of maximal plane graphs and pairs of non-crossing Dyck paths

DOI10.1016/j.disc.2004.01.021zbMath1070.05032OpenAlexW2007576514MaRDI QIDQ2566278

Nicolas Bonichon

Publication date: 22 September 2005

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2004.01.021

zbMATH Keywords

graph drawingrealizerSchnyder trees

Mathematics Subject Classification ID

Trees (05C05) Paths and cycles (05C38) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (16)

Dyck paths and pattern-avoiding matchings ⋮ On the number of planar Eulerian orientations ⋮ Catalan intervals and uniquely sorted permutations ⋮ Bijections for Weyl chamber walks ending on an axis, using arc diagrams and Schnyder woods ⋮ A bijection between a set of lexicographic semiorders and pairs of non-crossing Dyck paths ⋮ On the Number of α-Orientations ⋮ Bijections for Baxter families and related objects ⋮ Balanced Schnyder woods for planar triangulations: an experimental study with applications to graph drawing and graph separators ⋮ Toroidal maps: Schnyder woods, orthogonal surfaces and straight-line representations ⋮ A bijection between 2-triangulations and pairs of non-crossing Dyck paths ⋮ Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity ⋮ Random Generation and Enumeration of Proper Interval Graphs ⋮ Intervals in Catalan lattices and realizers of triangulations ⋮ Sampling and Counting 3-Orientations of Planar Triangulations ⋮ The generating function of planar Eulerian orientations ⋮ Bijective counting of plane bipolar orientations and Schnyder woods

Cites Work

• How to draw a planar graph on a grid
• Standard Young tableaux of height 4 and 5
• Planar graphs and poset dimension
• Output-sensitive reporting of disjoint paths
• Drawing planar graphs using the canonical ordering
• Vicious walkers and Young tableaux I: without walls
• On topological aspects of orientations
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