TOWARD AN UNCOUNTABLE ANALOGUE OF GALLAI'S THEOREM FOR COLORINGS OF THE PLANE

摘要

In this paper we prove that if S is any finite configuration of points in Z~2, then any finite coloring of E~2 must contain uncountably many monochromatic subsets homothetic to S. We extend a result of Brown, Dunfield, and Perry on 2-colorings of E~2 to any finite coloring of E~2.