Unit Disk Representations of Embedded Trees, Outerplanar and Multi-Legged Graphs
Computational Geometry
2021-08-27 v2 Discrete Mathematics
Abstract
A unit disk intersection representation (UDR) of a graph represents each vertex of as a unit disk in the plane, such that two disks intersect if and only if their vertices are adjacent in . A UDR with interior-disjoint disks is called a unit disk contact representation (UDC). We prove that it is NP-hard to decide if an outerplanar graph or an embedded tree admits a UDR. We further provide a linear-time decidable characterization of caterpillar graphs that admit a UDR. Finally we show that it can be decided in linear time if a lobster graph admits a weak UDC, which permits intersections between disks of non-adjacent vertices.
Keywords
Cite
@article{arxiv.2103.08416,
title = {Unit Disk Representations of Embedded Trees, Outerplanar and Multi-Legged Graphs},
author = {Sujoy Bhore and Maarten Löffler and Soeren Nickel and Martin Nöllenburg},
journal= {arXiv preprint arXiv:2103.08416},
year = {2021}
}
Comments
34 Pages, 19 Figures, An extended abstract of this paper will appear in the Proceedings of GD 2021