Solving Dominating Set in Larger Classes of Graphs: FPT Algorithms and Polynomial Kernels
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 bounded-degenerate graphs has a polynomial kernel, solving an open problem posed by Alon and Gutner in .
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- 3.Alon, N., Gutner, S.: Kernels for the dominating set problem on graphs with an excluded minor. Technical Report TR08-066, The Electronic Colloquium on Computational Complexity (ECCC) (2008)Google Scholar
- 4.Bodlaender, H.L., Downey, R.G., Fellows, M.R., Hermelin, D.: On problems without polynomial kernels (Extended abstract). In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 563–574. Springer, Heidelberg (2008)CrossRefGoogle Scholar
- 8.Dom, M., Lokshtanov, D., Saurabh, S.: Incompressibility through Colors and IDs. Accepted at ICALP 2009 (2009)Google Scholar