Positive dependence for colored percolation

For uniform random 4-colorings of graph edges with colors $\{a,b,c,d\}$, every two colors form a $\frac{1}{2}$- percolation, and every two overlapping pairs of colors form independent $\frac{1}{2}$-percolations. We show positive mutual dependence for pairs of colors $ab,ac$, and $ad$, and negative mutual dependence for pairs of colors $ab,ac$, and $bc$. The proof is based on a generalization of the Harris-Kleitman inequalities. We apply the results to crossing probabilities for the colored bond and site percolation, and to colored critical percolation that we also define.