Improved bounds for colouring circle graphs

TL;DR

This paper establishes an optimal up to constant factor chromatic bound for circle graphs based on their clique number, improving understanding of their coloring properties.

Contribution

It provides the first near-optimal chi-bounding function for circle graphs, advancing theoretical bounds in graph coloring.

Findings

Chromatic number bounded by 2ω log₂(ω) + 2ω log₂(log₂(ω)) + 10ω

First chi-bounding function for circle graphs that is optimal up to a constant

Improves theoretical understanding of circle graph coloring

Abstract

We prove the first $\chi$-bounding function for circle graphs that is optimal up to a constant factor. To be more precise, we prove that every circle graph with clique number at most $\omega$ has chromatic number at most $2\omega \log_2 (\omega) +2\omega \log_2(\log_2 (\omega)) + 10\omega$.