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Statement

Remark (p. 422). In the setting of Gallai's theorem, $n$ points in the plane not all on a line, $f(n)$ denotes the minimum number of lines that go through exactly two of the points. The paper states that it is not known whether $\lim f(n)=\infty$, and that all the authors can show is $f(n)\ge3$.

The bound $f(n)\ge3$ is asserted without proof; the paper gives none.

Source. N. G. de Bruijn and P. Erdős, On a combinatorial problem, Nederl. Akad. Wetensch., Proc. 51 (1948), 1277--1279 = Indag. Math. 10 (1948), 421--423, in the Indagationes page numbering: the remark on p. 422. The edition read is identified on the source card.

Read depth. Claims checked: the remark was read clause by clause on the printed page. There is no proof to check.

Bears on

• Problem 210: the remark poses the problem's first question, whether $f(n)\to\infty$, for the same quantity, and records the bound $f(n)\ge3$ without proof. It does not ask the problem's second question, how fast $f(n)$ grows. The answers recorded on the problem page come from later papers.