An annotated bibliography on 1-planarity |
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| Affiliation: | 1. Department of Computer Science, University of Arizona, Tucson, USA;2. Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy;1. College of Computers and IT, Taif University, Saudi Arabia;2. Department of Math. and CS, Faculty of Science, Beni-Suef University, Egypt;3. Department of Computer Science, Faculty of Science, Minia University, Egypt;1. I.K.G. Punjab Technical University, Kapurthala, Punjab, India;2. U.I.E.T., Panjab University, Chandigarh, India;1. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany;2. Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran;1. DEIB, Politecnico di Milano, via Ponzio 34/5, 20133 Milano, Italy;2. IEIIT, Consiglio Nazionale delle Ricerche, via Ponzio 34/5, 20133 Milano, Italy;1. Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, Japan;2. Department of Mathematics, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, Japan;1. School of Mathematics and Statistics, Shandong University, Weihai 264209, PR China;2. Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA |
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| Abstract: | The notion of 1-planarity is among the most natural and most studied generalizations of graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at most another edge. The study of 1-planar graphs dates back to more than fifty years ago and, recently, it has driven increasing attention in the areas of graph theory, graph algorithms, graph drawing, and computational geometry. This annotated bibliography aims to provide a guiding reference to researchers who want to have an overview of the large body of literature about 1-planar graphs. It reviews the current literature covering various research streams about 1-planarity, such as characterization and recognition, combinatorial properties, and geometric representations. As an additional contribution, we offer a list of open problems on 1-planar graphs. |
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| Keywords: | 1-planarity Beyond planar graphs Annotated bibliography |
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