Finding Induced Subgraphs via Minimal Triangulations

Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulation problems including Minimum Fill-in and Treewidth. We discover unexpected applications of these notions to the field of moderate exponential algorithms. In particular, we show that given an n-vertex graph G together with its set of potential maximal cliques, and an integer t, it is possible in time the number of potential maximal cliques times O(nO(t) ) to find a maximum induced subgraph of treewidth t in G and for a given graph F of treewidth t, to decide if G contains an induced subgraph isomorphic to F. Combined with an improved

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Fedor V. Fomin, Yngve Villanger
• Keywords: Maximal Cliques Times, Minimal Triangulation Problems, Potential Maximal Cliques, STACS 2010, Theoretical Computer Science