Erdős Problem #923 — Large-Chromatic Triangle-Free Subgraphs

For every set $V$ and every $n\in\mathbb{N}$, there exists $k\in\mathbb{N}$ such that every simple graph $G$ on $V$ with chromatic number at least $k$ contains a subgraph $H$ of $G$ satisfying

$$\chi(H)\ge n$$

and containing no clique of size $3$.