Crossing Stars in Topological Graphs
Gábor Tardos, Gézá Tóth · SIAM Journal on Discrete Mathematics · 2007
Let G be a graph without loops or multiple edges drawn in the plane. It is shown that, for any k, if G has at least $C_k n$ edges and n vertices, then it contains three sets of k edges, such that every edge in any of the sets crosses all edges in the other two sets. Furthermore, two of the three sets can be chosen such that all k edges in the set have a common vertex.