Monochromatic triangles in the max-norm plane

TL;DR

This paper investigates the minimum number of colors required to color the plane in a way that prevents monochromatic copies of any given non-degenerate triangle under the max-norm isometry.

Contribution

It provides a complete determination of the minimum coloring number for all non-degenerate triangles in the max-norm plane.

Findings

Exact minimum number of colors for various triangles

Characterization of triangles based on their max-norm isometric properties

Extension of geometric coloring theory to max-norm spaces

Abstract

For all non-degenerate triangles T, we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of T is monochromatic.