  Popielarz, Sahasrabudhe and Snyder in 2018 proved that maximal $K_{r+1}$-free
graphs with $(1-\frac{1}{r})\frac{n^2}{2}-o(n^{\frac{r+1}{r}})$ edges contain a
complete $r$-partite subgraph on $n-o(n)$ vertices. This was very recently
extended to odd cycles in place of $K_3$ by Wang, Wang, Yang and Yuan. We
further extend it to some other 3-chromatic graphs, and obtain some other
stability results along the way.
