This paper is concerned with the efficient computation of sparse Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of a graph coloring technique, bi-coloring, to exploit the sparsity of the Jacobian matrix $J$ and thereby allow for the efficient determination of $J$ using AD software. We analyze both a direct scheme and a substitution process. We discuss the results of numerical experiments indicating significant practical potential of this approach.