Creative Commons Attribution 4.0 license (CC BY 4.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2022.11
URN: urn:nbn:de:0030-drops-168090
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16809/
Angelini, Patrizio ; Bekos, Michael A. ; Katheder, Julia ; Kaufmann, Michael ; Pfister, Maximilian
RAC Drawings of Graphs with Low Degree
| pdf-format: |
|
Abstract
Motivated by cognitive experiments providing evidence that large crossing-angles do not impair the readability of a graph drawing, RAC (Right Angle Crossing) drawings were introduced to address the problem of producing readable representations of non-planar graphs by supporting the optimal case in which all crossings form 90° angles.In this work, we make progress on the problem of finding RAC drawings of graphs of low degree. In this context, a long-standing open question asks whether all degree-3 graphs admit straight-line RAC drawings. This question has been positively answered for the Hamiltonian degree-3 graphs. We improve on this result by extending to the class of 3-edge-colorable degree-3 graphs. When each edge is allowed to have one bend, we prove that degree-4 graphs admit such RAC drawings, a result which was previously known only for degree-3 graphs. Finally, we show that 7-edge-colorable degree-7 graphs admit RAC drawings with two bends per edge. This improves over the previous result on degree-6 graphs.
BibTeX - Entry
@InProceedings{angelini_et_al:LIPIcs.MFCS.2022.11,
author = {Angelini, Patrizio and Bekos, Michael A. and Katheder, Julia and Kaufmann, Michael and Pfister, Maximilian},
title = {{RAC Drawings of Graphs with Low Degree}},
booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages = {11:1--11:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-256-3},
ISSN = {1868-8969},
year = {2022},
volume = {241},
editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16809},
URN = {urn:nbn:de:0030-drops-168090},
doi = {10.4230/LIPIcs.MFCS.2022.11},
annote = {Keywords: Graph Drawing, RAC graphs, Straight-line and bent drawings}
}
| Keywords: | Graph Drawing, RAC graphs, Straight-line and bent drawings | |
| Seminar: | 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 22.08.2022 |
