Minimum fill-in and treewidth of split+ke and split+kv graphs

In this paper we investigate how graph problems that are NP-hard in general, but polynomially solvable on split graphs, behave on input graphs that are close to being split. For this purpose we define split+ke and split+kv graphs to be the graphs that can be made split by removing at most k edges and at most k vertices, respectively. We show that problems like treewidth and minimum fill-in are fixed parameter tractable with parameter k on split+ke graphs. Along with positive results of fixed parameter tractability of several problems on split+ke and split+kv graphs, we also show a surprising hardness result. We prove that computing the minimum fill-in of split+kv graphs is NP-hard even

• Type: Journal
• Year: 2010
• Where: DAM
• Authors: Federico Mancini
• Keywords: DAM 2010, Input Graphs, Minimum Fill-in, Split Graphs