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The Firefighter Problem models how a fire spreads on a graph while firefighters are being placed in an attempt to contain the fire. In this project, we use this model to examine how fires spread on the graphs of each of the eight semi-regular tessellations. Our goal is to determine the minimum number of firefighters needed to contain the fire. We first provide upper bounds on the number of firefighters needed to contain a fire on each semi-regular tessellation. We then establish a lower bound of one firefighter per turn for five of the eight semi-regular tessellations. We formulate a theorem for establishing lower bounds on a graph by using properties of geodesics and apply it successfully to the square grid. We then develop a labeling scheme for the movement of paths on 126.96.36.199 and classify geodesics on that graph.
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Merling, Lara Greta, "Fighting Fires on Semi-Regular Tessellations" (2014). Senior Projects Spring 2014. 140.