Spiraling and Folding: The Topological View

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.

• Publication year

  2022

• Venue

  Discrete & Computational Geometry

• Publication date

  2022-06-15

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1007/s00454-023-00603-zarXiv 2206.07849
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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