Drawing Graphs on Few Circles and Few Spheres
| Autor: | Alexander Wolff, Myroslav Kryven, Alex Ravsky |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
021103 operations research
Arboricity 0211 other engineering and technologies 0102 computer and information sciences 02 engineering and technology 01 natural sciences Graph Visual complexity Combinatorics Treewidth 010201 computation theory & mathematics Bipartite graph SPHERES Affine transformation Chromatic scale Mathematics |
| Zdroj: | Algorithms and Discrete Applied Mathematics ISBN: 9783319741796 CALDAM |
| Popis: | Given a drawing of a graph, its visual complexity is defined as the number of geometrical entities in the drawing, for example, the number of segments in a straight-line drawing or the number of arcs in a circular-arc drawing (in 2D). Recently, Chaplick et al. [4] introduced a different measure for the visual complexity, the affine cover number, which is the minimum number of lines (or planes) that together cover a crossing-free straight-line drawing of a graph G in 2D (3D). In this paper, we introduce the spherical cover number, which is the minimum number of circles (or spheres) that together cover a crossing-free circular-arc drawing in 2D (or 3D). It turns out that spherical covers are sometimes significantly smaller than affine covers. Moreover, there are highly symmetric graphs that have symmetric optimum spherical covers but apparently no symmetric optimum affine cover. For complete, complete bipartite, and platonic graphs, we analyze their spherical cover numbers and compare them to their affine cover numbers as well as their segment and arc numbers. We also link the spherical cover number to other graph parameters such as chromatic number, treewidth, and linear arboricity. |
| Databáze: | OpenAIRE |
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