@inproceedings{b8d826170a4a4c9c8e76296526f4528d,
title = "Unit Disk Representations of Embedded Trees, Outerplanar and Multi-legged Graphs",
abstract = "A unit disk intersection representation (UDR) of a graph G represents each vertex of G as a unit disk in the plane, such that two disks intersect if and only if their vertices are adjacent in G. 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.",
author = "Sujoy Bhore and Maarten L{\"o}ffler and Soeren Nickel and Martin N{\"o}llenburg",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 29th International Symposium on Graph Drawing and Network Visualization, GD 2021 ; Conference date: 14-09-2021 Through 17-09-2021",
year = "2021",
month = jan,
day = "1",
doi = "10.1007/978-3-030-92931-2\_22",
language = "English",
isbn = "9783030929305",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "304--317",
editor = "Purchase, \{Helen C.\} and Ignaz Rutter",
booktitle = "Graph Drawing and Network Visualization - 29th International Symposium, GD 2021, Revised Selected Papers",
address = "Germany",
}