The Firefighter problem: Saving sets of vertices on cubic graphs

Abstract

In the context of the Firefighter problem, a deterministic model of the spread of a fire or virus on a graph, SFIRE is the decision problem that asks if a specified set of vertices can be prevented from burning. We show SFIRE remains NP‐complete even when restricted to graphs with maximum degree 3 even when the fire starts at a vertex of degree 2.