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Solving Dominating Set in Larger Classes of Graphs: FPT Algorithms and Polynomial Kernels

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Philip, G., Raman, V., & Sikdar, S. (2009). Solving Dominating Set in Larger Classes of Graphs: FPT Algorithms and Polynomial Kernels. In A. Fiat, & P. Sanders (Eds.), Algorithms - ESA 2009 (pp. 694-705). Berlin: Springer. doi:10.1007/978-3-642-04128-0_62.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0019-DC09-F
Abstract
We show that the \nounk-Dominating Set} problem is fixed parameter tractable (FPT) and has a polynomial kernel for any class of graphs that exclude K_{i,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.