The firefighter problem for cubic graphs
نویسندگان
چکیده
منابع مشابه
The firefighter problem for cubic graphs
We show that the firefighter problem is NP-complete for cubic graphs. We also show that given a rooted tree of maximum degree three in which every leaf is the same distance from the root, it is NPcomplete to decide whether or not there is a strategy that protects every leaf from the fire, which starts at the root. By contrast, we describe a polynomial time algorithm to decide if it is possible ...
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We consider a dynamic problem introduced by B. Hartnell in 1995 [4]. Let (G, r) be a connected rooted graph (where r ∈ V (G)). At time 0, a fire breaks out at r. At each subsequent time interval, the firefighter defends some vertex which is not on fire, and then the fire spreads to all undefended neighbours of each burning (i.e., on fire) vertex. Once defended, a vertex remains so for all time ...
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We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time O(2) ≈ 1.260 and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound. We can also count or list all Hamiltonian cycles in a degree three graph in time O(2) ≈ 1.297. We also solve the traveling salesman problem in graphs of...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.05.007