Stabbing non-piercing sets and face lengths in large girth plane graphs
Dömötör Pálvölgyi, Kristóf Zólomy
Published: 2025/4/14
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 $\ell$.