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- W4317393955 abstract "We show that every complete n-vertex simple topological graph contains a topological subgraph on at least $$(log n)^{1/4 - o(1)}$$ vertices that is weakly isomorphic to the complete convex geometric graph or the complete twisted graph. This is the first improvement on the bound $$varOmega (log ^{1/8}n)$$ 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 $$(log n)^{1 -o(1)}$$ ." @default.
- W4317393955 created "2023-01-19" @default.
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- W4317393955 date "2023-01-01" @default.
- W4317393955 modified "2023-10-18" @default.
- W4317393955 title "Unavoidable Patterns in Complete Simple Topological Graphs" @default.
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- W4317393955 doi "https://doi.org/10.1007/978-3-031-22203-0_1" @default.
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