The one-firefighter containment conjecture for the strong grid

The strong grid is the graph obtained from the square grid by joining vertices that are at king-move distance one, so each vertex is adjacent also to its diagonal neighbours. In the Pyro game, firefighters protect vertices while the fire spreads to unprotected neighbouring vertices. Strong-grid containment conjecture. In the Pyro game, one firefighter cannot contain a fire on the strong grid. The source states that two firefighters suffice, while whether one firefighter suffices remains unknown; it therefore conjectures that one firefighter is insufficient.

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Primary source

Margaret-Ellen Messinger and Spencer Yarnell, “The Pyro game: a slow intelligent fire”, arXiv:2108.00101 (2021).

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