English

Pairwise intersecting convex sets and cylinders in $\R^3$

Combinatorics 2021-05-07 v2

Abstract

We prove that given a finite collection of cylinders in R3\R^3 with the property that any two them intersect, then there is a line intersecting an α\alpha fraction of the cylinders where α=128\alpha=\frac 1{28}. This is a special case of an interesting conjecture.

Keywords

Cite

@article{arxiv.2104.02148,
  title  = {Pairwise intersecting convex sets and cylinders in $\R^3$},
  author = {Imre Barany},
  journal= {arXiv preprint arXiv:2104.02148},
  year   = {2021}
}

Comments

6 pages

R2 v1 2026-06-24T00:52:06.676Z