English

Stabbing non-piercing sets and face lengths in large girth plane graphs

Combinatorics 2025-09-03 v2

Abstract

We show that a non-piercing family of connected planar sets with bounded independence number can be stabbed with a constant number of points. As a consequence, we answer a question of Axenovich, Kie{\ss}le and Sagdeev about the largest possible face length of an edge-maximal plane graph with girth at least \ell.

Keywords

Cite

@article{arxiv.2504.10618,
  title  = {Stabbing non-piercing sets and face lengths in large girth plane graphs},
  author = {Dömötör Pálvölgyi and Kristóf Zólomy},
  journal= {arXiv preprint arXiv:2504.10618},
  year   = {2025}
}
R2 v1 2026-06-28T22:58:15.754Z