Geodesic
On Strict (Outer-)Confluent Graphs
Journal of Graph Algorithms and Applications, Tome 25 (2021) no. 1, pp. 481-512.

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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.
DOI : 10.7155/jgaa.00568
Keywords: Strict confluent drawings, Intersection graphs, Unit-interval graphs, Bipartite permutation graphs, Cliquewidth, Cop-number 
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Henry Förster; Robert Ganian; Fabian Klute; Martin Nöllenburg. On Strict (Outer-)Confluent Graphs. Journal of Graph Algorithms and Applications, Tome 25 (2021) no. 1, pp. 481-512. doi : 10.7155/jgaa.00568. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00568/

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