Compressing Bounded Degree Graphs.

Recently, Aravind et al. (IPEC 2014) showed that for any finite set of connected graphs (mathcal {H}), the problem (mathcal {H})-Free Edge Deletion admits a polynomial kernelization on bounded degree input graphs. We generalize this theorem by no longer requiring the graphs in (mathcal {H}) to be connected. Furthermore, we complement this result by showing that also (mathcal {H})-Free Edge Editing admits a polynomial kernelization on bounded degree input graphs.