Minimal graphs that fold onto Kn

We disprove a conjecture of [Cook and Evans (1979)] by providing a number (the Stirling number of the second kind S(n, s) of them) of non-isomorphic s-chromatic graphs (s ⩾ 2) which fold onto Kn and are minimal in the number of vertices and edges. We also answer some other questions of [Cook and Evans (1979)].