  We introduce and investigate numerically a minimal class of dynamical
triangulations of two-dimensional gravity on the sphere in which only vertices
of order five, six or seven are permitted. We show firstly that this
restriction of the local coordination number, or equivalently intrinsic scalar
curvature, leaves intact the fractal structure characteristic of generic
dynamically triangulated random surfaces. Furthermore the Ising model coupled
to minimal two-dimensional gravity still possesses a continuous phase
transition. The critical exponents of this transition correspond to the usual
KPZ exponents associated with coupling a central charge c=1/2 model to
two-dimensional gravity.
