Compressing Bounded Degree Graphs

Recently, Aravind, Sandeep, and Sivadasan (IPEC 2014) showed that for any finite set of connected graphs H, the problem H-Free Edge Deletion admits a polynomial kernelization on bounded degree input graphs. We generalize this theorem by no longer requiring the graphs in H to be connected. Furthermore, we complement this result by showing that also H-Free Edge Editing admits a polynomial kernelization on bounded degree input graphs. We show that there exists a finite set H of connected graphs such that H-Free Edge Completion is incompressible even on input graphs of maximum degree 5, unless the polynomial hierarchy collapses to the third level. Under the same assumption, we show that C11-free Edge Deletion—as well as H-Free Edge Editing—is incompressible on 2-degenerate graphs.

• Type: Journal
• Year: 2016
• Where: LATIN
• Authors: Pål Grønås Drange, Markus S. Dregi, R. B. Sandeep
• Keywords: Information Technology, LATIN 2016