Problem 1208

For $d\geq 2$ let $F_d(n)$ be minimal such that every set of $n$ points in $\mathbb{R}^d$ contains a set of $F_d(n)$ points with distinct distances. Estimate $F_d(n)$ for fixed $d$ as $n\to \infty$ .

Source: erdosproblems.com/1208

Geometry
Distances

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CFGHUZ15: Conlon, David and Fox, Jacob and Gasarch, William and Harris, David G. and Ulrich, Douglas and Zbarsky, Samuel, Distinct volume subsets. SIAM J. Discrete Math. 29 (2015), 472-480.
Ch13: Charalambides, Marcos, A note on distinct distance subsets. J. Geom. (2013), 439-442.
ErGu70: Erdős, P. and Guy, R. K., Distinct distances between lattice points. Elem. Math. (1970), 121-123.
KSS75: Komlós, J. and Sulyok, M. and Szemeredi, E., Linear problems in combinatorial number theory. Acta Math. Acad. Sci. Hungar. (1975), 113-121.
LeTh95: Lefmann, Hanno and Thiele, Torsten, Point sets with distinct distances. Combinatorica (1995), 379-408.
Th95: T. Thiele, Geometric selection problems and hypergraphs. PhD thesis, Freir Universitat Berlin (1995).

Problem 1208

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