  Motivated in part by an observation that the zero forcing number for the
complement of a tree on $n$ vertices is either $n-3$ or $n-1$ in one
exceptional case, we consider the zero forcing number for the complement of
more general graphs under some conditions, particularly those that do not
contain complete bipartite subgraphs. We also move well beyond trees and
completely study all of the possible zero forcing numbers for the complements
of unicyclic graphs and cactus graphs.
