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. © 2013 Springer-Verlag.
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Cheong, O., Har-Peled, S., Kim, H., & Kim, H. S. (2013). On the number of edges of fan-crossing free graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8283 LNCS, pp. 163–173). https://doi.org/10.1007/978-3-642-45030-3_16
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