Drawing Trees and Cacti with Integer Edge Lengths on a Polynomial-Size Grid (Poster Abstract)
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Technical University of Munich, John Cabot University
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7080134095
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