On the Size of Planarly Connected Crossing GraphsAckerman, Eyal and Keszegh, Balázs and Vizer, Mate (2016) On the Size of Planarly Connected Crossing Graphs. In: Graph Drawing and Network Visualization. GD 2016, September, 19.  21., 2016 , pp. 311320(Official URL: http://dx.doi.org/10.1007/9783319501062_24). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319501062_24
AbstractWe prove that if an nvertex graph G can be drawn in the plane such that each pair of crossing edges is independent and there is a crossingfree edge that connects their endpoints, then G has O(n) edges. Graphs that admit such drawings are related to quasiplanar graphs and to maximal 1planar and fanplanar graphs.
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