Building Blocks of Upward Planar Digraphs
Journal of Graph Algorithms and Applications, Tome 11 (2007) no. 1, pp. 3-44.

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The upward planarity testing problem consists of testing if a digraph admits a drawing Γ such that all edges in Γ are monotonically increasing in the vertical direction and no edges in Γ cross. In this paper we reduce the problem of testing a digraph for upward planarity to the problem of testing if its blocks admit upward planar drawings with certain properties. We also show how to test if a block of a digraph admits an upward planar drawing with the aforementioned properties.
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     title = {Building {Blocks} of {Upward} {Planar} {Digraphs}},
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Patrick Healy; Karol Lynch. Building Blocks of Upward Planar Digraphs. Journal of Graph Algorithms and Applications, Tome 11 (2007) no. 1, pp. 3-44. doi : 10.7155/jgaa.00135. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00135/

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