Triangle colorings require at least seven colors

Abstract

We show that if a coloring of the plane has the properties that any two points at distance one are colored differently and the plane is partitioned into uniformly colored triangles under certain conditions, then it requires at least seven colors. This is also true for a coloring using uniformly colored polygons if it has a point bordering at least four polygons.

arXiv comment11 pages, 8 figures; revised argument in section 5, result extended to non-convex polygon colorings