Surviving Rates of Graphs with Bounded Treewidth for the Firefighter Problem
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چکیده
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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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 ve...
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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 for the firefighter problem to be the average percentage of vertices that can be saved when a fire s...
متن کاملThe Surviving Rate of a Graph for the Firefighter Problem
We consider the following firefighter problem on a graph G = (V, E). Initially, a fire breaks out at a vertex v of G. In each subsequent time unit, a firefighter protects one vertex, 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. Let sn(v) denote the maximum number of vertices the firefigh...
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Let k be an integer. Two vertex k-colorings of a graph are adjacent if they differ on exactly one vertex. A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent proper k-colorings. Any graph is (tw + 2)-mixing, where tw is the treewidth of the graph (Cereceda 2006). We prove that the shortest sequence between any two (tw + 2)-colorings is a...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2010
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100791130