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<p>In this work we address the Firefighter problem in graphs and its relationship with the bandwidth parameter <i>bw</i>(<i>G</i>) of a graph&#xa0;<i>G</i>. The Firefighter problem consists of a scenario in which a vertex <i>v</i> of the graph is initially set on fire and over time the fire spreads to unburned neighbours of vertices already on fire. The objective is to save the largest number of vertices by placing firefighters. After each placement, the fire spreads and this process continues until the fire is contained. By understanding the way the fire propagates on graphs of bounded bandwidth, we find a lower bound on the maximum number of vertices saved from fire in a graph.</p>

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Graphs of Small Bandwidth and the Firefighter Problem

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Sérgio Fusquino,
  • Diana Sasaki,
  • Vinicius dos Santos,
  • Diego Nicodemos

摘要

In this work we address the Firefighter problem in graphs and its relationship with the bandwidth parameter bw(G) of a graph G. The Firefighter problem consists of a scenario in which a vertex v of the graph is initially set on fire and over time the fire spreads to unburned neighbours of vertices already on fire. The objective is to save the largest number of vertices by placing firefighters. After each placement, the fire spreads and this process continues until the fire is contained. By understanding the way the fire propagates on graphs of bounded bandwidth, we find a lower bound on the maximum number of vertices saved from fire in a graph.