  Sturmfels-Sullivant conjectured that the cut polytope of a graph is normal if
and only if the graph has no K_5 minor. In the present paper, it is proved that
the normality of cut polytopes of graphs is a minor closed property. By using
this result, we have large classes of normal cut polytopes. Moreover, it turns
out that, in order to study the conjecture, it is enough to consider
4-connected plane triangulations.
