NP-Completeness of Some Tree-Clustering Problems
A graph is a tree of paths (cycles), if its vertex set can be partitioned into clusters, such that each cluster induces a simple path (cycle), and the clusters form a tree. Our main result states that the problem whether or not a given graph is a tree of paths (cycles) is NP-complete. Moreover, if the length of the paths (cycles) is bounded by a constant, the problem is in P.
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