ISAAC 2013: Algorithms and Computation pp 163-173

# On the Number of Edges of Fan-Crossing Free Graphs

• Otfried Cheong
• Sariel Har-Peled
• Heuna Kim
• Hyo-Sil Kim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

## Abstract

A graph drawn in the plane with n vertices is fan-crossing free if there is no triple of edges e,f and g, such that e and f have a common endpoint and g crosses both e and f. We prove a tight bound of 4n − 9 on the maximum number of edges of such a graph for a straight-edge drawing. The bound is 4n − 8 if the edges are Jordan curves. We also discuss generalizations to monotone graph properties.

### Keywords

graph theory graph drawing planar graph extremal graph

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## Authors and Affiliations

• Otfried Cheong
• 1
• Sariel Har-Peled
• 2
• Heuna Kim
• 3
• Hyo-Sil Kim
• 4
1. 1.Department of Computer ScienceKAISTDaejeonKorea
2. 2.Department of Computer ScienceUniversity of IllinoisUrbanaUSA
3. 3.Freie Universität BerlinBerlinGermany
4. 4.Department of Computer Science and EngineeringPOSTECHPohangKorea