• Corpus ID: 222291324

Firefighting on the Hexagonal Grid and on Infinite Trees

  title={Firefighting on the Hexagonal Grid and on Infinite Trees},
  author={Abdullah Dean and Sean English and Tongyun Huang and Robert A. Krueger and Andy Lee and Mose Mizrahi and Casey Wheaton-Werle},
  journal={arXiv: Combinatorics},
The firefighter problem with $k$ firefighters on an infinite graph $G$ is an iterative graph process, defined as follows: Suppose a fire breaks out at a given vertex $v\in V(G)$ on Turn 1. On each subsequent even turn, $k$ firefighters protect $k$ vertices that are not on fire, and on each subsequent odd turn, any vertex that is on fire spreads the fire to all adjacent unprotected vertices. The firefighters' goal is to eventually stop the spread of the fire. If there exists a strategy for $k… 

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