Duffy, Christopher2011-09-022011-09-0220112011-09-02http://hdl.handle.net/1828/3550The Firefighter Process models the spread and defence of a fire using a simple graph. We consider the following discrete-time process: at t = 0 some vertex of the graph begins burning. At each subsequent step we may defend a vertex from burning and the fire spreads from all burning vertices to all undefended neighbours. We consider the related problems of maximising the number of saved vertices, protecting a specified set from burning and maximising the weight of the saved vertices. We close three open problems concerning these decision problems and their related optimisation problems using the notion of a strategy, the sequence of defended vertices.enGraph TheoryComplexityFirefighterThesisAvailable to the World Wide Web