D. Eppstein, D. Holten, M. Löffler, M. Nöllenburg, B. Speckmann, K. Verbeek:

"Strict Confluent Drawing";

Journal of Computational Geometry,7(2016), 1; 22 - 46.

We define strict confluent drawing, a form of confluent drawing in which the

existence of an edge is indicated by the presence of a smooth path through a system of arcs

and junctions (without crossings), and in which such a path, if it exists, must be unique.

We prove that it is NP-complete to determine whether a given graph has a strict confluent

drawing but polynomial to determine whether it has an outerplanar strict confluent drawing

with a fixed vertex ordering (a drawing within a disk, with the vertices placed in a given

order on the boundary).

http://publik.tuwien.ac.at/files/PubDat_249242.pdf

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