Abstract
We prove that if an n-vertex graph G can be drawn in the plane such that each pair of crossing edges is independent and there is a crossing-free edge that connects their endpoints, then G has O(n) edges. Graphs that admit such drawings are related to quasi-planar graphs and to maximal 1-planar and fan-planar graphs.
| Original language | English |
|---|---|
| Pages (from-to) | 11-22 |
| Number of pages | 12 |
| Journal | Journal of Graph Algorithms and Applications |
| Volume | 22 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2018 |
Bibliographical note
Funding Information:Most of this work was done during a visit of the first author to the Rényi Institute that was partially supported by the National Research, Development and Innovation Office – NKFIH under the grant PD 108406 and by the ERC Advanced Research Grant no. 267165 (DIS-CONV). The second author was supported by the NKFIH under the grant PD 108406 and K 116769 and by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The third author was supported by the NKFIH under the grant SNN 116095. E-mail addresses: ackerman@sci.haifa.ac.il (Eyal Ackerman) keszegh.balazs@renyi.mta.hu (Balázs Keszegh) vizermate@gmail.com (Mate Vizer)
Publisher Copyright:
© 2018, Brown University. All rights reserved.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)
- Computer Science Applications
- Geometry and Topology
- Computational Theory and Mathematics