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On Planar Straight-Line Dominance Drawings

Authors Patrizio Angelini , Michael A. Bekos , Giuseppe Di Battista , Fabrizio Frati , Luca Grilli , Giacomo Ortali

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Graph algorithms
Keywords
  • st-graphs
  • dominance drawings
  • planar straight-line drawings
  • upward planarity

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Abstract

We study the following question, which has been considered since the 90’s: Does every st-planar graph admit a planar straight-line dominance drawing? We show concrete evidence for the difficulty of this question, by proving that, unlike upward planar straight-line drawings, planar straight-line dominance drawings with prescribed y-coordinates do not always exist and planar straight-line dominance drawings cannot always be constructed via a contract-draw-expand inductive approach. We also show several classes of st-planar graphs that always admit a planar straight-line dominance drawing. These include st-planar 3-trees in which every stacking operation introduces two edges incoming into the new vertex, st-planar graphs in which every vertex is adjacent to the sink, and st-planar graphs in which no face has the left boundary that is a single edge.

Cite As Get BibTex

Patrizio Angelini, Michael A. Bekos, Giuseppe Di Battista, Fabrizio Frati, Luca Grilli, and Giacomo Ortali. On Planar Straight-Line Dominance Drawings. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.5

Author Details

Patrizio Angelini
  • John Cabot University, Rome, Italy
Michael A. Bekos
  • University of Ioannina, Greece
Giuseppe Di Battista
  • Università degli Studi Roma Tre, Rome, Italy
Fabrizio Frati
  • Università degli Studi Roma Tre, Rome, Italy
Luca Grilli
  • Università degli Studi di Perugia, Italy
Giacomo Ortali
  • Università degli Studi di Perugia, Italy

Funding

  • Di Battista, Giuseppe: Supported by the European Union, Next Generation EU, Mission 4, Component 1, CUP C53D23003680006 PRIN project no. 2022TS4Y3N "EXPAND: scalable algorithms for EXPloratory Analyses of heterogeneous and dynamic Networked Data".
  • Frati, Fabrizio: Supported by the European Union, Next Generation EU, Mission 4, Component 1, CUP J53D23007130006 PRIN proj. 2022ME9Z78 "NextGRAAL: Next-generation algorithms for constrained GRAph visuALization".
  • Grilli, Luca: Supported by MUR PNRR project SERICS (COVERT: CUP_J93C23002310006), funded by the European Union – Next Generation EU.

Acknowledgements

This research initiated at the First Summer Workshop on Graph Drawing (SWGD 2021). Thanks to the organizers and the participants for an inspiring atmosphere.

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