On the Number of Edges of Fan-Crossing Free Graphs
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.
Keywordsgraph theory graph drawing planar graph extremal graph
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