  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, while the positive zero forcing number is an upper bound on the minimum
number of induced trees 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.
