Area stability of plank covers

Egor Bakaev; Amir Yehudayoff

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arXiv · 2609.30409

Area stability of plank covers

Egor Bakaev·Amir Yehudayoff

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Abstract

We prove a conjecture of András Bezdek on the stability of plank covers of the planar disk $D$. Namely, we show that if a sufficiently small concentric disk $rD$ is removed from $D$, then every finite family of planks covering the resulting annulus can be re-arranged to cover the whole disk. For the proof, we show a strong stability result for a related covering problem. If the hole has area $a \geq 0$ then the total overlap is $\geq c a/r$ where $c>0$ is a constant. This overlap estimate is not specific to the disk and is applicable to all planar symmetric convex bodies. We develop two new ingredients: a pruning procedure and a flattening mechanism.

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BibTeX RIS

Egor Bakaev, Amir Yehudayoff. 2026-09-24. Area stability of plank covers. https://arxiv.org/abs/2609.30409

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