Petruska's question on planar convex sets
| Autor: | Jobson, Adam S., K��zdy, Andr�� E., Lehel, Jen��, Pervenecki, Timothy J., T��th, G��za |
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| Rok vydání: | 2019 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1912.08080 |
| Popis: | Given $2k-1$ convex sets in $R^2$ such that no point of the plane is covered by more than $k$ of the sets, is it true that there are two among the convex sets whose union contains all $k$-covered points of the plane? This question due to Gy. Petruska has an obvious affirmative answer for $k=1,2,3$; we show here that the claim is also true for $k=4$, and we present a counterexample for $k=5$. We explain how Petruska's geometry question fits into the classical hypergraph extremal problems, called arrow problems, proposed by P. Erd��s. 13 pages |
| Databáze: | OpenAIRE |
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