On the Surviving Rate of Graphs with Bounded Treewidth
نویسندگان
چکیده
The firefighter problem is a discrete-time game on graphs introduced by Hartnell in an attempt to model the spread of fire, diseases, computer viruses and suchlike in a macro-control level. To measure the defence ability of a graph as a whole, Cai and Wang defined the surviving rate of a graph G, which is the average percentage of vertices that can be saved when a fire starts randomly at one vertex of G. In this paper we prove that if k firefighters are available in each round, the surviving rate of graphs with treewidth no more than k approaches one when the number of vertices of the graph tends to infinity.
منابع مشابه
Surviving Rates of Graphs with Bounded Treewidth for the Firefighter Problem
The firefighter problem is the following discrete-time game on a graph. Initially, a fire starts at a vertex of the graph. In each round, a firefighter protects one vertex not yet on fire, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefighter is to save as many vertices as possible. The surviving rate of a graph is the average percentag...
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