
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.
Euclidean Ramsey, Euclidean plane, Computational Theory and Mathematics, translates, Ramsey theory, Discrete Mathematics and Combinatorics, configuration, Ramsey, Theoretical Computer Science
Euclidean Ramsey, Euclidean plane, Computational Theory and Mathematics, translates, Ramsey theory, Discrete Mathematics and Combinatorics, configuration, Ramsey, Theoretical Computer Science
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| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
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