On disjoint covers and ROBDD size

The relation between the number of nodes in a ROBDD and the number of implicants in the disjoint cover of the function represented by that ROBDD is studied. We identify a class of functions for which there are disjoint covers such that a cover of a larger size can be represented by a ROBDD with a smaller number of nodes. This shows that the size of a ROBDD is not a monotonically increasing function of the size of the disjoint cover.