Abstract
AbstractFor 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 \(2^{o(k)}\cdot |G|^{O(1)}\), unless Exponential Time Hypothesis fails.KeywordsRegular GraphInput GraphStar GraphEdge DeletionVertex DeletionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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