Abstract
We study the complexity of turning a given graph, by edge editing, into a target graph whose critical-clique graph is any fixed graph. The problem came up in practice, in an effort of mining huge word similarity graphs 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.
Highlights
Graphs in this paper are undirected and have no loops or multiple edges
The bound is tight: We show that the base of k/c cannot beat the base in the best fixedparameter tractable (FPT) algorithm for Vertex Cover
The following observation is known for Cluster Editing due to [10]; here we show it for general H
Summary
Graphs in this paper are undirected and have no loops or multiple edges. In an edge modification problem, an input graph must be modified by edge insertions or deletions or both, to get a target graph with some prescribed property. For any fixed graph H, our target graphs will be the graphs obtained from H by replacing vertices with bags of true twins Our motivation of this type of problem is the concise description of graphs with very few cliques (that may overlap) and some extra or missing edges. Experience in our project shows that some existing standard clustering methods generate poor word clusters which are either too small or dragged out and not internally dense This suggested the idea of defining the clusters directly by the desired properties, and to determine them by edge editing of candidate subgraphs. On the positive side, they are in SUBEPT
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