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Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid (Poster Abstract)

Authors Henry Förster , Stephen Kobourov , Jacob Miller , Johannes Zink

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LIPIcs.GD.2025.48.pdf
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ACM Subject Classification
  • Mathematics of computing → Trees
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Harborth’s conjecture
  • tree drawings
  • cactus drawings
  • grid drawings

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Abstract

A strengthened version of Harborth’s well-known conjecture - known as Kleber’s conjecture - states that every planar graph admits a planar straight-line drawing where every edge has integer length and each vertex is restricted to the integer grid. Positive results for Kleber’s conjecture are known for planar 3-regular graphs, for planar graphs that have maximum degree 4, and for planar 3-trees. However, all but one of the existing results are existential and do not provide bounds on the required grid size. We provide polynomial-time algorithms for computing crossing-free straight-line drawings of trees and cactus graphs with integer edge lengths and integer vertex position on polynomial-size integer grids. We also give an historic overview of planar straight-line graph drawing results.

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Henry Förster, Stephen Kobourov, Jacob Miller, and Johannes Zink. Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 48:1-48:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.48

Author Details

Henry Förster
  • Technical University of Munich, Germany
Stephen Kobourov
  • Technical University of Munich, Germany
Jacob Miller
  • Technical University of Munich, Germany
Johannes Zink
  • Technical University of Munich, Germany

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