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In this paper we solve, for triconnected digraphs, the problem of the existence of a P-time algorithm for testing if a digraph has an upward drawing, i.e. a drawing such that all the edges point upward. The problem arises in the fields of ordered sets and automatic graph drawing and was open from several years. The time complexity of the proposed algorithm is O(n + r3/ogr), where n is the number of vertices and r is the number of sources and sinks of the digraph.

On upward drawing testing of triconnected digraphs (extended abstract)