The chromatic symmetric function conjecture for triangle-free graphs

Let $G$ and $H$ be simple, triangle-free graphs, and let $X_G$ and $X_H$ denote their chromatic symmetric functions.

Triangle-free graph conjecture. If

$$X_G=X_H,$$

then $G$ and $H$ are isomorphic.

This would substantially strengthen the conjecture that the chromatic symmetric function distinguishes nonisomorphic trees, since trees are triangle-free. The paper presents it as a direction for further research based on computational data and construction results.