We study Hartnell's firefighter problem on infinite trees and characterise the branching number in terms of the firefighting game. Using our results about trees, we give a partial answer to a question of Mart\'inez-Pedroza concerning firefighting on Cayley graphs.
Cite
@article{arxiv.1707.01224,
title = {Firefighting on trees and Cayley graphs},
author = {Florian Lehner},
journal= {arXiv preprint arXiv:1707.01224},
year = {2017}
}