A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
Bipolar orientations revisited
Discrete Applied Mathematics - Special issue: Fifth Franco-Japanese Days, Kyoto, October 1992
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
Proceedings of the 7th conference on Formal power series and algebraic combinatorics
Intervals in Catalan lattices and realizers of triangulations
Journal of Combinatorial Theory Series A
Straight-line drawing of quadrangulations
GD'06 Proceedings of the 14th international conference on Graph drawing
Partitions of graphs into trees
GD'06 Proceedings of the 14th international conference on Graph drawing
New bijective links on planar maps via orientations
European Journal of Combinatorics
Bijections for Baxter families and related objects
Journal of Combinatorial Theory Series A
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A bijection @F is presented between plane bipolar orientations with prescribed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with prescribed extremities. This yields a combinatorial proof of the following formula due to Baxter for the number @Q"i"j of plane bipolar orientations with i non-polar vertices and j inner faces: @Q"i"j=2(i+j)!(i+j+1)!(i+j+2)!i!(i+1)!(i+2)!j!(j+1)!(j+2)!. In addition, it is shown that @F specializes into the bijection of Bernardi and Bonichon between Schnyder woods and non-crossing pairs of Dyck words. This is the extended and revised journal version of a conference paper with the title ''Bijective counting of plane bipolar orientations'', which appeared in Electr. Notes in Discr. Math. pp. 283-287 (Proceedings of Eurocomb'07, 11-15 September 2007, Sevilla).