Kernelization and Sparseness: the Case of Dominating Set

We prove that for every positive integer r and for every graph class G of bounded expansion, the r-Dominating Set problem admits a linear kernel on graphs from G. Moreover, in the ∗ The research of P. Drange, F. Fomin, M. Pilipczuk, and M. Pilipczuk leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 267959. Mi. Pilipczuk currently holds a post-doc position at Warsaw Centre of Mathematics and Computer Science, and is supported by the Foundation for Polish Science. F. Reidl, F. Villaamil, and S. Sikdar are supported by DFG-Project RO 927/13-1 “Pragmatic Parameterized Algorithms”. M. Dregi and D. Lokshtanov are supported by the BeHard grant under the recruitment programme of the of Bergen Research Foundation. S. Saurabh is supported by PARAPPROX, ERC starting grant no. 306992. S. Kreutzer has been supported by the ERC under the EU’s Horizon 2020 res...

• Type: Journal
• Year: 2016
• Where: STACS
• Authors: Pål Grønås Drange, Markus Sortland Dregi, Fedor V. Fomin, Stephan Kreutzer, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Felix Reidl, Fernando Sanchez Villaamil, Saket Saurabh, Sebastian Siebertz, Somnath Sikdar
• Keywords: STACS 2016, Theoretical Computer Science