# Circle graphs are quadratically $\chi$-bounded

## TL;DR

This paper proves that the chromatic number of circle graphs can be bounded quadratically in terms of their clique number, specifically at most 7 times the square of the clique number.

## Contribution

It establishes a quadratic upper bound on the chromatic number for circle graphs based on their clique number, advancing understanding of graph coloring.

## Key findings

- Chromatic number of circle graphs is at most 7 times the square of the clique number.
- Provides a quadratic $ ext{chi}$-boundedness result for circle graphs.
- Improves previous bounds on coloring circle graphs.

## Abstract

We prove that the chromatic number of a circle graph with clique number $\omega$ is at most $7\omega^2$.