License: Creative Commons Attribution 4.0 International 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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16809/
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Angelini, Patrizio ; Bekos, Michael A. ; Katheder, Julia ; Kaufmann, Michael ; Pfister, Maximilian

RAC Drawings of Graphs with Low Degree

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LIPIcs-MFCS-2022-11.pdf (0.8 MB)

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
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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