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On Strict (Outer-)Confluent Graphs

  • Henry Förster
  • Robert Ganian
  • Fabian KluteEmail author
  • Martin Nöllenburg
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

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 (\(\varDelta \)-)SOC graphs have bounded cliquewidth.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of TübingenTübingenGermany
  2. 2.Algorithms and Complexity GroupTU WienViennaAustria

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