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  1. (, Graph Drawing and Network Visualization: 30th International Symposium, GD 2022, Tokyo, Japan, September 13–16, 2022, Revised Selected Papers)
    Angelini, P. (Ed.)
    We show that every complete n-vertex simple topological graph contains a topological subgraph on at least (logn)1/4−o(1) vertices that is weakly isomorphic to the complete convex geometric graph or the complete twisted graph. This is the first improvement on the bound Ω(log1/8n) obtained in 2003 by Pach, Solymosi, and Tóth. We also show that every complete n-vertex simple topological graph contains a plane path of length at least (logn)1−o(1) . 
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