Does Eulerian percolation on $Z^2$ percolate ?
  Eulerian percolation on Z 2 with parameter p is the classical Bernoulli bond percolation with parameter p conditioned on the fact that every site has an even degree. We first explain why Eulerian percolation with parameter p coincides with the contours of the Ising model for a well-chosen parameter $\beta$(p). Then we study the percolation properties of Eulerian percolation. 
Olivier Garet (IECL), Regine Marchand (IECL), Ir\`ene Marcovici (IECL)
math.PR