Thrackle

A thrackle is a good drawing in which every pair of distinct edges meets exactly once, either at a common endpoint or at a proper graph crossing. A graph is thrackleable if it admits such a drawing. The Conway thrackle conjecture asserts that a thrackle has no more edges than vertices.

Simon (2026) proved that a thrackle on vertices has at most edges, where is the floor function. Simon (2026) reports AI assistance with the proof and computational checks.