Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond
نویسندگان
چکیده
منابع مشابه
Polynomial Kernels for Dominating Set in $K_{i,j}$-free and d-degenerate Graphs
We show that for any fixed i, j ≥ 1, the k-Dominating Set problem restricted to graphs that do not have Ki,j as a subgraph is fixed parameter tractable (FPT) and has a polynomial kernel. This result implies that this problem restricted to bounded-degenerate graphs has a polynomial kernel, solving an open problem posed by Alon and Gutner in [3]. Our result extends the class of graphs for which t...
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The domination number of a graph G = (V,E) is the minimum size of a dominating set U ⊆ V , which satisfies that every vertex in V \U is adjacent to at least one vertex in U . The notion of a problem kernel refers to a polynomial time algorithm that achieves some provable reduction of the input size. Given a graph G whose domination number is k, the objective is to design a polynomial time algor...
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We show that the k-Dominating Set problem is fixed parameter tractable (FPT) and has a polynomial kernel for any class of graphs that exclude Ki,j as a subgraph, for any fixed i, j ≥ 1. This strictly includes every class of graphs for which this problem has been previously shown to have FPT algorithms and/or polynomial kernels. In particular, our result implies that the problem restricted to bo...
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In standard kernelization algorithms, the usual goal is to reduce, in polynomial time, an instance (I, k) of a parameterized problem to an equivalent instance (I ′, k′) of size bounded by a function in k. One of the central problems in this area, whose investigation has led to the development of many kernelization techniques, is the Dominating Set problem. Given a graph G and k ∈ N, Dominating ...
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2012
ISSN: 1549-6325,1549-6333
DOI: 10.1145/2390176.2390187