Editing the simplest graphs

Paper in proceedings, 2014

We study the complexity of editing a graph into a target graph with any fixed critical-clique graph. The problem came up in practice, in mining a huge word similarity graph for well structured word clusters. It also adds to the rich field of graph modification problems. We show in a generic way that several variants of this problem are in SUBEPT. As a special case, we give a tight time bound for edge deletion to obtain a single clique and isolated vertices, and we round up this study with NP-completeness results for a number of target graphs.