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 .
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}
}