  We introduce and solve a two-matrix model for the tri-coloring problem of the
vertices of a random triangulation. We present three different solutions: (i)
by orthogonal polynomial techniques (ii) by use of a discrete Hirota bilinear
equation (iii) by direct expansion. The model is found to lie in the
universality class of pure two-dimensional quantum gravity, despite the
non-polynomiality of its potential.
