**Strict confluent drawing**.

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

arXiv:1308.6824.

*21st Int. Symp. Graph Drawing*, Bordeaux, France, 2013.

Springer,*Lecture Notes in Comp. Sci.*8242, 2013, pp. 352–363.

*J. Computational Geometry*7 (1): 22–46, 2016.A confluent drawing of a graph is a set of points and curves in the plane with the property that two vertices are adjacent in the graph if and only if the corresponding points can be connected to each other by smooth paths in the drawing. We define a variant of confluent drawing, strict confluent drawing, in which a smooth path between two vertices (if it exists) must be unique. We show that it is NP-complete to test whether such drawings exist, in contrast to unrestricted confluence for which the complexity remains open. Additionally, we show that finding outerplanar drawings (in which the points are on the boundary of a disk and the curves are interior to it) with a fixed cyclic vertex ordering can be performed in polynomial time. We use circle packings to find nice versions of these drawings in which all tracks are represented by piecewise-circular curves.

Co-authors – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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