# A coloring of the plane without monochromatic right triangles

## TL;DR

This paper proves that under the Continuum Hypothesis, it is possible to color the plane with countably many colors without creating a monochromatic right triangle, resolving a previously claimed result.

## Contribution

It provides a complete and correct proof of a coloring of the plane avoiding monochromatic right triangles under the Continuum Hypothesis, clarifying earlier claims.

## Key findings

- Existence of a coloring with no monochromatic right triangles under CH
- Complete proof of the coloring construction
- Addresses and corrects previous claims by Erdős and Komjáth

## Abstract

We give a full, correct proof of the following result, earlier claimed by Erd\H{o}s and Komj\'ath. If the Continuum Hypothesis holds then there is a coloring of the plane with countably many colors, with no monocolored right triangle.