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Simple $k$-Planar Graphs are Simple $(k+1)$-Quasiplanar
- Source :
- Journal of Combinatorial Theory. Series B, 142
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
Abstract
- A simple topological graph is $k$-quasiplanar ($k\geq 2$) if it contains no $k$ pairwise crossing edges, and $k$-planar if no edge is crossed more than $k$ times. In this paper, we explore the relationship between $k$-planarity and $k$-quasiplanarity to show that, for $k \geq 2$, every $k$-planar simple topological graph can be transformed into a $(k+1)$-quasiplanar simple topological graph.<br />Comment: arXiv admin note: substantial text overlap with arXiv:1705.05569
- Subjects :
- Beyond planarity
Computational Geometry (cs.CG)
FOS: Computer and information sciences
Discrete Mathematics (cs.DM)
0102 computer and information sciences
Edge (geometry)
01 natural sciences
Theoretical Computer Science
Combinatorics
Topological graphs
symbols.namesake
Simple (abstract algebra)
FOS: Mathematics
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
0101 mathematics
Mathematics
Graph drawing
k-Planar graphs
k-Quasiplanar graphs
010102 general mathematics
Topological graph
Planar graph
Computational Theory and Mathematics
010201 computation theory & mathematics
symbols
Computer Science - Computational Geometry
Pairwise comparison
Combinatorics (math.CO)
Computer Science - Discrete Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Journal of Combinatorial Theory. Series B, 142
- Accession number :
- edsair.doi.dedup.....77940d67d9214d91a677268db6fdbb2c
- Full Text :
- https://doi.org/10.48550/arxiv.1909.00223