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A k-quasiplanar graph is a graph drawn in the plane with no k pairwise crossing edges. Pach, Shahrokhi, and Szegedy conjectured that every such graph on n vertices has Oₖ(n) edges. ChatGPT produced a proof of this conjecture. Here, we present a simplified, self-contained version of that proof.
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Pach et al. (2026) studied this question.
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