Hamiltonian cycles on random Eulerian triangulations

A random Eulerian triangulation is a random triangulation where an even num ber of triangles meet at any given vertex, We argue that the central charge increases by one if the fully packed O(n) model is defined on a random Eul erian triangulation instead of an ordinary random triangulation. Considerin g the case n --> 0, this implies that the system of random Eulerian triangu lations equipped with Hamiltonian cycles describes a c = -1 matter field co upled to 2D quantum gravity as opposed to the system of usual random triang ulations equipped with Hamiltonian cycles which has c = -2. Hence, in this case one should see a change in the entropy exponent from the value gamma = -1 to the irrational value gamma = 1/6 (-1 - root 13) = -0.76759... when g oing from a usual random triangulation to an Eulerian one, A direct enumera tion of configurations confirms this change in gamma. (C) 1999 Elsevier Sci ence B.V.