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.
This research was supported in part by NRF grant 2011-0016434 and in part by NRF grant 2011-0030044 (SRC-GAIA), both funded by the government of Korea.
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Cheong, O., Har-Peled, S., Kim, H., Kim, HS. (2013). On the Number of Edges of Fan-Crossing Free Graphs. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_16
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DOI: https://doi.org/10.1007/978-3-642-45030-3_16
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