Blanchard Ph., Gandolfo D., Ruiz J., Shlosman S. On the Euler--Poincar\'e Characteristic of the Random Cluster Model (976K, ps) ABSTRACT. Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. We present here new results about the behaviour of the Euler characteristic of the clusters of the (Fortuin--Kasteleyn) random cluster measure.