  Zero forcing is a combinatorial game played on a graph with a goal of turning
all of the vertices of the graph black while having to use as few "unforced"
moves as possible. This leads to a parameter known as the zero forcing number
which can be used to give an upper bound for the maximum nullity of a matrix
associated with the graph.
  We introduce a new variation on the zero forcing game which can be used to
give an upper bound for the maximum nullity of a matrix associated with a graph
that has $q$ negative eigenvalues. This gives some limits to the number of
positive eigenvalues that such a graph can have and so can be used to form
lower bounds for the inertia set of a graph.
