On Structural Parameterizations of Firefighting

The Firefighting problem is defined as follows. At time Open image in new window , a fire breaks out at a vertex of a graph. At each time step Open image in new window , a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all undefended neighbors from the vertices on fire. This process stops when the fire cannot spread anymore. The goal is to find a sequence of vertices for the firefighter that maximizes the number of saved (non burned) vertices.