Characterization of Ramsey configurations

Characterize exactly which finite configurations are Ramsey in Euclidean space.

Background

The paper reviews classical Euclidean Ramsey theory, noting that all Ramsey sets are spherical and that products of Ramsey sets remain Ramsey. It also describes soluble and subsoluble sets, which form a broad class of known Ramsey configurations. Despite these results, the complete classification of Ramsey configurations is unresolved.