Monochromatic translates of configurations in the plane (Q5929841)

It is shown that every admissible red-blue coloring of the Euclidean plane, i.e.~every red-blue coloring for which no two blue points are distance 1 apart, has a red translate of every three point configuration. On the other hand, a seven-point configuration and an admissible red-blue coloring of the plane are specified so that the seven-point configuration is forbidden in the red set. Relations to earlier work of \textit{R. Juhász} [J. Comb. Theory, Ser. A 27, 152-160 (1979; Zbl 0431.05001)] who considered congruent copies of configurations instead of translates are highlighted.