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A bijection $\Phi$ is presented between plane bipolar orientations with prescribed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with prescribed extremities.
On the enumeration of rooted nonseparable maps
W. G. Brown and W.T. Tutte · 1964
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An algorithm for planarity testing of graphs
A. Lempel, S. Even, and I. Cederbaum · 1967
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A linear algorithm for embedding planar graphs using pq-trees
N. Chiba, T. Nishizeki, S. Abe, and T. Ozawa · 1985
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Binomial determinants, paths, and hook formulae
I. Gessel and X. Viennot · 1985
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A unified approach to visibility representations of planar graphs
R. Tamassia and I. G. Tollis · 1986
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Determinants, paths, and plane partitions, 1989
I. Gessel and X. Viennot · 1989
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Planar grid embedding in linear time
R. Tamassia and I. G. Tollis · 1989
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Orientations bipolaires
P. Ossona de Mendez · 1994
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Bipolar orientations revisited
H. De Fraysseix, P. Ossona de Mendez, and P. Rosenstiehl · 1995
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Regular edge labeling of 4 4 -connected plane graphs and its applications in graph drawing problems
G. Kant and X. He · 1997
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Baxter permutations
S. Dulucq and O. Guibert · 1998
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R. J. Baxter · 2001
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Four classes of pattern-avoiding permutations under one roof: Generating trees with two labels
M. Bousquet-Mélou · 2002
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A bijection between realizers of maximal plane graphs and pairs of non-crossing dyck paths
N. Bonichon · 2005
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Straight-line drawing of quadrangulations
É. Fusy · 2006
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A binary labelling for plane laman graphs and quadrangulations
C. Huemer and S. Kappes · 2006
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Partitions of graphs into trees
T. Biedl and F. J. Brandenburg · 2007
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Baxter permutations and plane bipolar orientations
N. Bonichon, M. Bousquet-Mélou, and É. Fusy · 2008
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Bijections for baxter families and related objects
S. Felsner, É. Fusy, M. Noy, and D. Orden · 2008
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S. Felsner · 2004
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Intervals in catalan lattices and realizers of triangulations
O. Bernardi and N. Bonichon · 2009
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