We introduce a matrix model describing the fully packed O(n) model on rando
m Eulerian triangulations (i.e. triangulations with all vertices of even va
lency). For n = 1 the model is mapped onto a particular gravitational 6-ver
tex model with central charge c = 1, hence displaying the expected shift c
--> c + 1 when going from ordinary random triangulations to Eulerian ones.
The case of arbitrary n is also discussed. (C) 1999 Elsevier Science B.V. A
ll rights reserved.