On the Size of Planarly Connected Crossing Graphs

Ackerman, 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. 311-320(Official URL: http://dx.doi.org/10.1007/978-3-319-50106-2_24).

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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.

Item Type: Conference Paper
Classifications: G Algorithms and Complexity > G.420 Crossings
Z Theory > Z.750 Topology
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1551

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