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Corpus ID: 222291324

Firefighting on the Hexagonal Grid and on Infinite Trees

@article{Dean2020FirefightingOT,
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},
year={2020}
}

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… Expand

The paper concludes with a collection of 26 open problems and possible research projects for The Firefighter Problem, which has attracted considerable attention since being introduced in 1995.Expand

It is proved that, for any orientation, a singleFirefighters problem on orientations of the grid whose edges correspond to a tiling of the plane with regular hexagons is investigated.Expand

On any turn, at most k trees can have firefighters placed on them, so if there is a point in time where there are more than k(n − t) subtrees with burning roots and only n −