Beyond Planar Graphs: Introduction
Recent research topics in topological graph theory and graph drawing generalize the notion of planarity to sparse non-planar graphs called beyond planar graphs with forbidden crossing patterns. In this chapter, we introduce various types of beyond planar
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Beyond Planar Graphs Communications of NII Shonan Meetings
Beyond Planar Graphs
Seok-Hee Hong Takeshi Tokuyama •
Editors
Beyond Planar Graphs Communications of NII Shonan Meetings
123
Editors Seok-Hee Hong School of Computer Science University of Sydney Sydney, NSW, Australia
Takeshi Tokuyama School of Science and Technology Kwansei Gakuin University Sanda, Hyogo, Japan
ISBN 978-981-15-6532-8 ISBN 978-981-15-6533-5 https://doi.org/10.1007/978-981-15-6533-5
(eBook)
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Preface
Most real-world data sets are relational, which can be modeled as graphs, consisting of vertices and edges. Planar graphs are fundamental for both Graph Theory and Graph Algorithms, and extensively studied: structural properties and fundamental algorithms for planar graphs have been discovered. However, most real-world graphs, such as social networks and biological networks, are non-planar. To analyze and visualize such real-world networks, we need to solve fundamental mathematical and algorithmic research questions on sparse non-planar graphs, called beyond planar graphs. Recently, research topics in topological graph theory generalize the notion of planarity to beyond-planar graphs, i.e., non-planar graphs with topological constraints such as specific types of crossings, or with forbidden crossing patterns. Examples include: • k-planar graphs, which can be embedded with at most k crossings per edge; • k-quasi-planar graphs, which can be embedded without k mutually crossing edges. Consequently, combinatorics (such as edge density), algorithmics (such as testing/embedding algorithms), and geometr
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