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A One-Page Solution of a Problem of Erdős and Purdy


The following theorem was conjectured by Erdős and Purdy: Let P be a set of \(n>4\) points in general position in the plane. Suppose that R is a set of points disjoint from P such that every line determined by P passes through a point in R. Then \(|R| \ge n\). In this paper we give a very elegant and elementary proof of this, being a very good candidate for the “book proof” of this conjecture.

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We thank Gábor Tardos for a clever remark that helped to shorten the presentation of the proof.

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Correspondence to Rom Pinchasi.

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Editor in Charge: Kenneth Clarkson

Dedicated to the memory of Branko Grünbaum.

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R. Pinchasi: Supported by ISF Grant (Grant No. 409/16). A. Polyanskii: Supported in part by the Leading Scientific Schools of Russia through Grant No. NSh-6760.2018.1.

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Pinchasi, R., Polyanskii, A. A One-Page Solution of a Problem of Erdős and Purdy. Discrete Comput Geom 64, 382–385 (2020).

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