For a graph H, the H-free Edge Deletion problem asks whether there exist at most k edges whose deletion from the input graph G results in a graph without any induced copy of H. We prove that H-free Edge Deletion is NP-complete if H is a graph with at least two edges and H has a component with maximum number of vertices which is a tree or a regular graph. Furthermore, we obtain that these NP-complete problems cannot be solved in parameterized subexponential time, i.e., in time 2o(k)⋅|G|O(1), unless Exponential Time Hypothesis fails.
CITATION STYLE
Aravind, N. R., Sandeep, R. B., & Sivadasan, N. (2015). Parameterized lower bound and np-completeness of some h-free edge deletion problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9486, pp. 424–438). Springer Verlag. https://doi.org/10.1007/978-3-319-26626-8_31
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