Remarks on monochromatic configurations for finite colorings of the plane


Gurevich had conjectured that for any finite coloring of the Euclidean plane, there always exists a triangle of unit area with monochromatic vertices. Graham ([5], [6]) gave the first proof of this conjecture; a much shorter proof has been obtained recently by Dumitrescu and Jiang [4]. A similar result in the case of a trapezium, claimed by the present authors in [3] does not hold due to an error and a weaker result is recovered for quadrilaterals in this paper. We also take up the original question of triangles

DOI Code: 10.1285/i15900932v32n2p83

Keywords: Gurevich’s conjecture; van der Waerden’s theorem; Monochromatic configurations

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