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Kynčl, Jan; Schaefer, Marcus; Sedgwick, Eric; Štefankovič, Daniel
Discrete & computational geometry, 07/2024, Volume: 72, Issue: 1Journal Article
For every n , we construct two arcs in the plane that intersect at least n times and do not form spirals. The construction is in three stages: we first exhibit two closed curves on the torus that do not form double spirals, then two arcs on the torus that do not form spirals, and finally two arcs in the plane that do not form spirals. The planar arcs provide a counterexample to a proof of Pach and Tóth concerning string graphs.
