Just Accepted
This paper has been accepted to be published in the JGAA Special Issue on Graph Drawing Beyond Planarity. The paper will receive a volume, an issue number, and page numbers when the whole special issue will be published.
On the size of planarly connected crossing graphs
Eyal Ackerman, Bal√°zs Keszegh, and Mate Vizer
Vol. 0, no. 0, pp. 0-0, 0. Regular paper.
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.
Submitted: April 2017.
Reviewed: June 2017.
Revised: July 2017.
Accepted: July 2017.
Final: July 2017.
Appeared on-line: October 2017.
article (PDF)