Erdős, Paul, Some of my favorite solved and unsolved problems in graph theory. Quaestiones Math. 16 (1993), 333--350; Chapter IV, printed p. 341. Erdős poses the question in the words "Is there a 4-chromatic critical graph on $n$ vertices every vertex of which has degree $>\epsilon n$ (for some $\epsilon>0$)", says he asked it more than twenty years earlier, and notes that Dirac's original example is $6$-chromatic critical with every degree above $n/2$. He reports the problem still open for $4$- and $5$-chromatic graphs, and names the independent constructions of Simonovits [36] and Toft [37] of $4$-chromatic critical graphs on $n$ vertices with every degree greater than $cn^{1/3}$ as the best result known to him. The site cites p. 341 ([Er93,p.341]), where the library card locates the passage. Library home: Erdős 1993.

Simonovits, M., On colour-critical graphs. Studia Sci. Math. Hungar. (1972), 67-81.

Toft, B., Two theorems on critical $4$-chromatic graphs. Studia Sci. Math. Hungar. (1972), 83-89.