# Upward drawings of triconnected digraphs

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DOI: 10.1007/BF01188716

- Cite this article as:
- Bertolazzi, P., Battista, G.D., Liotta, G. et al. Algorithmica (1994) 12: 476. doi:10.1007/BF01188716

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## Abstract

A polynomial-time algorithm for testing if a triconnected directed graph has an upward drkwing is presented. An upward drkwing is a planar drkwing such that all the edges flow in a common direction (e.g., from bottom to top). The problem arises in the fields of automatic graph drkwing and ordered sets, and has been open for several years. The proposed algorithm is based on a new combinatorial characterization that maps the problem into a max-flow problem on a sparse network; the time complexity is*O(n+r*^{2)}, where*n* is the number of vertices and*r* is the number of sources and sinks of the directed graph. If the directed graph has an upward drkwing, the algorithm allows us to construct one easily.

### Key words

PlanarityAutomatic graph drkwingHierarchical structuresMax-flow*st*-DigraphsAcyclic digraphsOrdered sets