Chromatic Extremal Thresholds and the Multipartite $K_4$-Free Problem

For positive integers $n,r,t$, let $δ(n,r,t)$ denote the maximum possible minimum degree of a balanced $r$-partite graph with parts of size $n$ and chromatic number at most $t$. Lo, Treglown and Zhao established a general upper bound for this parameter and used it, together with explicit constructio