Finite Euclidean Ramsey theory (Q1906140)

The author studies some problems of Euclidean Ramsey theory. He shows that in any two-coloring of the points of \(\mathbb{R}^4\) there will be four points forming a monochromatic unit square. He also improves the lower bounds for the chromatic numbers of the unit distance graphs of \(\mathbb{R}^4\) and \(\mathbb{R}^5\) to 7 and 9, respectively.