Counting colored random triangulations Original Research Article

We revisit the problem of enumeration of vertex-tricolored planar random triangulations solved in [Nucl. Phys. B 516 [FS] (1998) 543–587] in the light of recent combinatorial developments relating classical planar graph counting problems to the enumeration of decorated trees. We give a direct combinatorial derivation of the associated counting function, involving tricolored trees. This is generalized to arbitrary k-gonal tessellations with cyclic colorings and checked by use of matrix models.