A generalization of the firefighter problem on z × z

Authors:
K. L. Ng;P. Raff
Affiliations:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore;Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

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 32, then a fire starting at any finite number of vertices in the two dimensional infinite grid graph can always be contained.