The Firefighter problem on graph classes
نویسندگان
چکیده
منابع مشابه
The 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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In this paper we study the complexity of the firefighter problem and related problems on trees when more than one firefighter is available at each time step, and answer several open questions of [8]. More precisely, when b ≥ 2 firefighters are allowed at each time step, the problem is NP-complete for trees of maximum degree b+2 and polynomial-time solvable for trees of maximum degree b + 2 when...
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The dynamics of infectious diseases spread is crucial in determining their risk and offering ways to contain them. We study sequential vaccination of individuals in networks. In the original (deterministic) version of the Firefighter problem, a fire breaks out at some node of a given graph. At each time step, b nodes can be protected by a firefighter and then the fire spreads to all unprotected...
متن کاملOn the Maximum Number of Dominating Classes in Graph Coloring
In this paper we investigate the dominating- -color number، of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].
متن کاملThe Firefighter Problem: A Structural Analysis
We consider the complexity of the firefighter problem where a budget of b ≥ 1 firefighters are available at each time step. This problem is proved to be NP-complete even on trees of degree at most three and b = 1 [10] and on trees of bounded degree b+3 for any fixed b ≥ 2 [3]. In this paper, we provide further insight into the complexity landscape of the problem by showing a complexity dichotom...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2016
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.11.024