Firefighting on trees and Cayley graphs
F Lehner - arXiv preprint arXiv:1707.01224, 2017 - arxiv.org
arXiv preprint arXiv:1707.01224, 2017•arxiv.org
… 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 Martínez-Pedroza concerning firefighting on Cayley graphs. … We
show that for a Cayley graph with exponential growth of rate α we have λc = α. This implies that …
number in terms of the firefighting game. Using our results about trees, we give a partial
answer to a question of Martínez-Pedroza concerning firefighting on Cayley graphs. … We
show that for a Cayley graph with exponential growth of rate α we have λc = α. This implies that …
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.
arxiv.org
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