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Layered Polyline Drawings of Planar Graphs

Author Debajyoti Mondal

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LIPIcs.GD.2025.34.pdf
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ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
Keywords
  • Layered Drawing
  • Variable Embedding
  • Polyline Drawing
  • Cycle Separator

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Abstract

A k-layer polyline drawing of a planar graph G is a planar drawing of G on a set L of k parallel lines such that each vertex is mapped to a point on L and each edge is mapped to a polygonal chain with the endpoints and bends lying on L. In the fixed embedding setting, the output drawing maintains the given planar embedding, whereas in the variable embedding setting, the embedding may change. Every n-vertex planar graph admits a polyline drawing on 2n/3 layers, which is the best known upper bound for both settings. We improve this bound in the variable embedding setting. We show that every planar graph can be drawn on 14n/27+O(√n) layers by choosing a proper planar embedding, breaking the long-standing 2n/3-layer barrier.

Cite As Get BibTex

Debajyoti Mondal. Layered Polyline Drawings of Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 34:1-34:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.34

Author Details

Debajyoti Mondal
  • Department of Computer Science, University of Saskatchewan, Saskatoon, Canada

Acknowledgements

The research is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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