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Source. Conjecture 4 on p. 3 of Ron Graham and Eric Tressler, Open problems in Euclidean Ramsey theory, in A. Soifer (ed.), Ramsey Theory: Yesterday, Today, and Tomorrow, Progress in Mathematics, Birkhäuser (2011), 115--120, doi:10.1007/978-0-8176-8092-3_7. Page numbers here are those of the authors' preprint, the edition read, as identified on the source card.

Statement

Conjecture 4 (p. 3, quoted). "($100). Every 4-point subset of a circle is Ramsey."

The paper calls it weaker than Conjecture 3; a subset of a circle is spherical. Ramsey is meant in the sense of p. 1. Kříž's Theorem 2, as reported, covers the 4-point subsets of a circle that are the vertices of a trapezoid.

After it (p. 3) the paper asks, for a Ramsey set $X$ and an integer $r$, what can be said about the least dimension $N(X,r)$, and calls this a major open question already for two-point sets.

Read depth. Claims checked: the statement was read on p. 3 of the preprint.

Bears on

• Problem 174: a special case of the characterisation question, for four points on a circle. The paper poses it as a conjecture.