  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.
