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A generalization of the firefighter problem on $\mathbb Z \times \mathbb Z$. (English)
Discrete Appl. Math. 156, No. 5, 730-745 (2008).
Summary: We consider a generalization of the firefighter problem where the number of firefighters available per time step $t$ is not a constant. We show that if the number of firefighters available is periodic in $t$ and the average number per time period exceeds $\frac 3 2$, then a fire starting at any finite number of vertices in the two dimensional infinite grid graph can always be contained.