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Fixed-parameter tractability of graph modification problems for hereditary properties. (English) Zbl 0875.68702
Summary: This paper is concerned with the fixed-parameter tractability of the problem of deciding whether a graph can be made into a graph with a specified hereditary property by deleting at most i vertices, at most j edges, and adding at most k edges, where i,j,k are fixed integers. It is shown that this problem is fixed-parameter tractable whenever the hereditary property can be characterized by a finite set of forbidden induced subgraphs. Furthermore, the problem of deciding whether a graph can be made into a chordal graph by adding a fixed number k of edges is shown to be solvable in O$$(4^{k}(k+1)^{-3/2}(m+n))$$ time, and is thus fixed-parameter tractable.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science
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