Distance-Restricted Firefighting on Finite Graphs
Abstract
In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph and then firefighters protect vertices. On each subsequent turn, the fire spreads to the collective unburned neighbourhood of all the burning vertices and the firefighters again protect vertices. Once a vertex has been burned or protected it remains that way for the rest of the game. In \textit{distance-restricted firefighting} the firefighters' movement is restricted so they can only move up to some fixed distance and they may or may not be permitted to move through burning vertices. In this paper we establish the NP-completeness of the distance-restricted versions of {\sc -Firefighter} and present an integer program for computing the exact value. We also discuss some interesting properties of the \textit{Expected Damage} function.
Cite
@article{arxiv.2306.12575,
title = {Distance-Restricted Firefighting on Finite Graphs},
author = {Andrea C. Burgess and John Hawkin and Alexander Howse and John Marcoux and David A. Pike},
journal= {arXiv preprint arXiv:2306.12575},
year = {2025}
}