Research output per year
Research output per year
Steven Chaplick, Fabian Lipp, Alexander Wolff, Johannes Zink^{*}
Research output: Contribution to journal › Article › Academic › peer-review
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 (beyond-planar graphs is a collective term for the primary attempts to generalize the planar graphs) 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) x O(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)) x O(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. (C) 2019 Elsevier B.V. All rights reserved.
Original language | English |
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Pages (from-to) | 50-68 |
Number of pages | 19 |
Journal | Computational Geometry |
Volume | 84 |
DOIs | |
Publication status | Published - Nov 2019 |
Externally published | Yes |
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review
Research output: Working paper / Preprint › Preprint