@inproceedings{5229aff31e504b7bb6423f0ee8a48537,
title = "Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends",
abstract = "We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two pairs of crossing edges share two vertices.We study the relations of these beyond-planar graph classes to right-angle crossing (RAC) graphs that admit compact drawings on the grid with few bends. We present four drawing algorithms that preserve the given embeddings. First, we show that every n-vertex NIC-planar graph admits a NIC-planar RAC drawing with at most one bend per edge on a grid of size O(n)xO(n). Then, we show that every n-vertex 1-planar graph admits a 1-planar RAC drawing with at most two bends per edge on a grid of size O(n(3))xO(n(3)). Finally, we make two known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at most one bend per edge and for drawing IC-planar RAC graphs straight-line.",
author = "Steven Chaplick and Fabian Lipp and Alexander Wolff and Johannes Zink",
note = "DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",
year = "2018",
doi = "10.1007/978-3-030-04414-5_10",
language = "English",
series = "Lecture Notes in Computer Science",
publisher = "Springer, Cham",
pages = "137--151",
editor = "T. Biedl and A. Kerren",
booktitle = "Graph Drawing and Network Visualization. GD 2018",
address = "Switzerland",
}