Abstract
Let S be an n-punctured sphere with . We prove that is the maximum size of a family of pairwise nonhomotopic simple arcs on S joining a fixed pair of distinct punctures of S and pairwise intersecting at most twice. On the way, we show that a square annular diagram A has a corner on each of its boundary paths if A contains at least one square and the dual curves of A are simple arcs joining the boundary paths of A and pairwise intersecting at most once.
Citation
Sami Douba. "2-Systems of Arcs on Spheres with Prescribed Endpoints." Michigan Math. J. 71 (2) 321 - 346, May 2022. https://doi.org/10.1307/mmj/20195794
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