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Petruska's Question on Planar Convex Sets by Jobson, Adam S.; Kézdy, André E.; Lehel, Jenő; Pervenecki, Timothy J.; Tóth, Géza is a scholarly article available to read on EtoBox.

What is Petruska's Question on Planar Convex Sets about?

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\H{o}s.

Author

Jobson, Adam S.; Kézdy, André E.; Lehel, Jenő; Pervenecki, Timothy J.; Tóth, Géza

Published

2019

Language

EN