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Title: Edge deletion problems : branching facilitated by modular decomposition
Authors: Liu, YL
Wang, JX
You, J
Chen, JE
Cao, YX 
Keywords: Graph modification problems
Edge deletion problems
Chain graphs
Trivially perfect graphs
Modular decomposition
Issue Date: 2015
Publisher: Elsevier
Source: Theoretical computer science, 2015, v. 573, p. 63-70 How to cite?
Journal: Theoretical computer science 
Abstract: Edge deletion problems ask for a minimum set of edges whose deletion makes a graph have a certain property. When this property can be characterized by a finite set of forbidden induced subgraphs, the problem can be solved in fixed-parameter time by a naive bounded search tree algorithm. Sometimes deleting an edge to break an erstwhile forbidden induced subgraph might introduce new ones, which may involve the neighbors of the original forbidden induced subgraph. Therefore, in considering possible ways to break a forbidden induced subgraph one naturally takes its neighborhood into consideration. This observation easily yields more efficient branching rules, but a naive implementation will require too many tedious case analyses. Here we take advantage of modular decomposition, which allows us to focus on far simpler quotient graphs instead of the original graphs. They together yield simple improved algorithms for the edge deletion problems to chain graphs and trivially perfect graphs.
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.01.049
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