Abstract
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 K i,j as a subgraph, for any fixed i,jāā„ā1. 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 [3].
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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: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_62
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DOI: https://doi.org/10.1007/978-3-642-04128-0_62
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