Remarks on monochromatic configurations for finite colorings of the plane

Authors

  • Sukumar Das Adhikari
  • P. Rath

DOI:

https://doi.org/10.1285/i15900932v32n2p83

Keywords:

Gurevich’s conjecture, van der Waerden’s theorem, Monochromatic configurations

Abstract

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

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Published

01-06-2013

Issue

Volume 32, Issue 2 (2012)

Section

Articoli

License

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