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Problem 99 — Erdős Problems

Problem 99

Let $A\subseteq\mathbb{R}^2$ be a set of $n$ points with minimum distance equal to 1, chosen to minimise the diameter of $A$ . If $n$ is sufficiently large then must there be three points in $A$ which form an equilateral triangle of size 1?

Source: erdosproblems.com/99

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BeFo99: Bezdek, András and Fodor, Ferenc, Minimal diameter of certain sets in the plane. J. Combin. Theory Ser. A (1999), 105-111.
Er94b: Erdős, Paul, Some problems in number theory, combinatorics and combinatorial geometry. Math. Pannon. (1994), 261-269.

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Status: Open
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