Solving dominating set in larger classes of graphs: Fpt algorithms and polynomial kernels

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,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 [3]. © 2009 Springer Berlin Heidelberg.