  In this paper, we study existential monadic second order (EMSO) properties of
undirected graphs. In 2001, J.-M. Le Bars proved that there exists an EMSO
sentence about undirected graphs such that the probability that it is true does
not converge (here, the probability distribution is uniform over the set of all
graphs on the fixed set of vertices). In the same paper, he conjectured that,
for EMSO sentences with 2 first order variables, the 0-1 law holds (every
sentence is either true asymptotically almost surely (a.a.s.), or false
a.a.s.). We give an example of EMSO sentence with 1 monadic variable without
convergence and an example of EMSO sentence with 3 first order variables
without convergence.
