On Strict (Outer-)Confluent Graphs
Vol. 25, no. 1, pp. 481-512, 2021. Regular paper.
Abstract 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 ($\Delta$-)SOC graphs have bounded cliquewidth.

 This work is licensed under the terms of the CC-BY license.
Submitted: December 2020.
Reviewed: April 2021.
Revised: July 2021.
Accepted: August 2021.
Final: August 2021.
Published: September 2021.
Communicated by William S. Evans
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