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The crossing lemma: every graph with n vertices and m ≥ 4n edges has crossing number cr(G) = Ω(m³/n²). Covers the lemma's statement, proofs, constants and improvements (e.g. Pach–Tóth), sharpness constructions, and direct applications such as Székely-type bounds. Claims about named problems the lemma is applied to keep their own tags; general graph theory stays under Graph theory.

Every graph with n vertices and m ≥ 4n edges has crossing number Ω(m^3/n^2).

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Graph theoryimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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