Solid coverings of the Euclidean plane with incongruent circles (Q1971506)

A set of closed circles (circular discs) is a covering of the Euclidean plane if every point of the plane belongs to at least one of the circles. L. Fejes Tóth introduced the notion of solidity: a covering is solid if no finite number of its members can be rearranged so as to form, together with the rest of the members, a covering not congruent to the original one. In the present paper the authors consider coverings of the plane by circles of two different sizes. They establish a sufficient condition for such a covering to be solid, and as an application of this general theorem prove that there exist infinitely many coverings of this kind. The introduction contains a fine survey of the state of this problem (solid coverings by incongruent circles) and the related solid packings. Also, there is a substantial useful bibliography and a clear, readable text.