Solving Dominating Set in Larger Classes of Graphs: FPT Algorithms and Polynomial Kernels
نویسندگان
چکیده
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 boundeddegenerate graphs has a polynomial kernel, solving an open problem posed by Alon and Gutner in [3].
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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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