An Upper bound on the chromatic number of circle graphs without $K_4$

TL;DR

This paper establishes an upper bound of 30 on the chromatic number of circle graphs that do not contain a clique of size four, advancing understanding of coloring constraints in such graphs.

Contribution

The paper provides a new upper bound on the chromatic number for circle graphs without $K_4$, which was previously unknown.

Findings

Chromatic number of such graphs is at most 30

No circle graph without $K_4$ requires more than 30 colors

Improves bounds on coloring circle graphs without large cliques

Abstract

Let $G$ be a circle graph without clique on 4 vertices. We prove that the chromatic number of $G$ doesn't exceed 30.