Deciding ffn(G) <= m is NP-hard, shortest strategies on complete binary trees have superpolynomial length, with almost sharp bounds for those trees and transfer of results to the Hunter and Rabbit game.
Every complete binary treeT= (V, E)hasmax v∈V δ(v)≤3≤dand can therefore be extended to ad-regularG ′ for everyd∈N ≥3, see [12]
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Complexity of Firefighting on Graphs
Deciding ffn(G) <= m is NP-hard, shortest strategies on complete binary trees have superpolynomial length, with almost sharp bounds for those trees and transfer of results to the Hunter and Rabbit game.