  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.
