On Star-Cover and Path-Cover of a Tree

We study two restricted versions of the Subforest Isomorphism problem, the Star-Cover of a Tree (SCT) and the Path-Cover of a Tree (PCT) problems. Both problems are NP-complete. The problems are closely related to a number of well-studied problems, including the problems Subgraph Isomorphism, Tree Editing, and Graph Packing. We show that the problems SCT and PCT are fixed-parameter tractable. Thorough development of parameterized algorithms and kernelization algorithms for these problems are presented.

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