It is shown that every 2-planar graph is quasiplanar, that is, if a simple graph admits a drawing in the plane such that every edge is crossed at most twice, then it also admits a drawing in which no three edges pairwise cross. We further show that quasiplanarity is witnessed by a simple topological drawing, that is, any two edges cross at most once and adjacent edges do not cross.
@InProceedings{hoffmann_et_al:LIPIcs.MFCS.2017.47, author = {Hoffmann, Michael and T\'{o}th, Csaba D.}, title = {{Two-Planar Graphs Are Quasiplanar}}, booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, pages = {47:1--47:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-046-0}, ISSN = {1868-8969}, year = {2017}, volume = {83}, editor = {Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.47}, URN = {urn:nbn:de:0030-drops-80811}, doi = {10.4230/LIPIcs.MFCS.2017.47}, annote = {Keywords: graph drawing, near-planar graph, simple topological plane graph} }
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