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H. Förster, R. Ganian, F. Klute, M. Nöllenburg:
"On Strict (Outer-)Confluent Graphs";
Journal of Graph Algorithms and Applications, 25 (2021), 1; S. 481 - 512.

A strict confluent (SC) graph drawing is a drawing of a graph with vertices
as points in the plane, where vertex adjacencies are represented not by individual
curves but rather by unique smooth paths through a planar system of junctions and
arcs. If all vertices of the graph lie in the outer face of the drawing, the drawing is
called a strict outerconfluent (SOC) drawing. SC and SOC graphs were first considered
by Eppstein et al. in Graph Drawing 2013. Here, we establish several new relationships
between the class of SC graphs and other graph classes, in particular string graphs and
unit-interval graphs. Further, we extend earlier results about special bipartite graph
classes to the notion of strict outerconfluency, show that SOC graphs have cop number
two, and establish that tree-like (Δ-)SOC graphs have bounded cliquewidth.

http://dx.doi.org/10.7155/jgaa.00568

https://publik.tuwien.ac.at/files/publik_299983.pdf