Let G be any connected graph on n vertices, n ≥ 2. Let k be any positive integer. Suppose that a fire breaks out on some vertex of G. Then in each turn k firefighters can protect vertices of G — each can protect one vertex not yet on fire; Next a fire spreads to all unprotected neighbours. The k-surviving rate of G, denoted by ρ k (G), is the expected fraction of vertices that can be saved from the fire by k firefighters, provided that the starting vertex is chosen uniformly at random. In this… CONTINUE READING