Layered Fan-Planar Graph Drawings

Authors Therese Biedl , Steven Chaplick , Michael Kaufmann , Fabrizio Montecchiani , Martin Nöllenburg , Chrysanthi Raftopoulou

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Author Details

Therese Biedl
  • University of Waterloo, Canada
Steven Chaplick
  • Maastricht University, The Netherlands
Michael Kaufmann
  • Universität Tübingen, Germany
Fabrizio Montecchiani
  • Universitá degli Studi di Perugia, Italy
Martin Nöllenburg
  • TU Wien, Austria
Chrysanthi Raftopoulou
  • National Technical University of Athens, Greece


Research initiated while Fabrizio Montecchiani was visiting the University of Waterloo and continued at the Bertinoro Workshop on Graph Drawing 2018.

Cite AsGet BibTex

Therese Biedl, Steven Chaplick, Michael Kaufmann, Fabrizio Montecchiani, Martin Nöllenburg, and Chrysanthi Raftopoulou. Layered Fan-Planar Graph Drawings. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. In this paper, we study fan-planar drawings that use h (horizontal) layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter tractable in h, via a reduction to a similar result for planar graphs by Dujmović et al. If the embedding is not fixed, then we give partial results for h = 2: It was already known how to test the existence of fan-planar proper 2-layer drawings for 2-connected graphs, and we show here how to test this for trees. Along the way, we exhibit other interesting results for graphs with a fan-planar proper h-layer drawing; in particular we bound their pathwidth and show that they have a bar-1-visibility representation.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Graph algorithms
  • Graph Drawing
  • Parameterized Complexity
  • Beyond Planar Graphs


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