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arXiv · 2504.10618

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

Dömötör Pálvölgyi·Kristóf Zólomy
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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, Kießle and Sagdeev about the largest possible face length of an edge-maximal plane graph with girth at least $\ell$.

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Dömötör Pálvölgyi, Kristóf Zólomy. 2025-08-30. Stabbing non-piercing sets and face lengths in large girth plane graphs. https://arxiv.org/abs/2504.10618

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