On some problems of Euclidean Ramsey theory

2015/07/09 by Ilya D. Shkredov, Shkredov, Ilya D.
Mathematics · #05B25 #05D10 #11T24 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05B25 #msc:05D10 #msc:11T24

paper · pdf · doi:10.48550/arxiv.1507.02727

10 pages

arxiv created 2015/07/22 · arxiv updated 2015/07/24

Abstract

In the paper we prove, in particular, that for any measurable coloring of the euclidian plane into two colours there is a monochromatic triangle with some restrictions on the sides. Also we consider similar problems in finite fields settings.

Related

• A Euclidean Ramsey result in the plane
• Canonical theorems in geometric Ramsey theory
• Improved lower bound on an Euclidean Ramsey problem
• Euclidean Gallai-Ramsey Theory
• Canonical Ramsey: triangles, rectangles and beyond