### Abstract:

The zero forcing number and the positive zero forcing number of a graph are
two graph parameters that arise from two types of graph colourings. The zero
forcing number is an upper bound on the minimum number of induced paths in
the graph that cover all the vertices of the graph, while the positive zero forcing
number is an upper bound on the minimum number of induced trees in the
graph needed to cover all the vertices in the graph. We show that for a block-
cycle graph the zero forcing number equals the path cover number. We also
give a purely graph theoretical proof that the positive zero forcing number of
any outerplanar graphs equals the tree cover number of the graph. These ideas
are then extended to the setting of k-trees, where the relationship between the
positive zero forcing number and the tree cover number becomes more complex.