Arcs on spheres intersecting at most twice
Geometric Topology
2017-07-26 v1
Abstract
Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set of arcs pairwise intersecting at most once, which start at p and end in Q, is |X|(|X| + 1). We deduce that the maximal cardinality of a set of arcs with arbitrary endpoints pairwise intersecting at most twice is |X|(|X| + 1)(|X| + 2).
Keywords
Cite
@article{arxiv.1707.07818,
title = {Arcs on spheres intersecting at most twice},
author = {Christopher Smith and Piotr Przytycki},
journal= {arXiv preprint arXiv:1707.07818},
year = {2017}
}
Comments
22 pages, 18 figures