Abstract
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.
The work of the author was supported by the German Research Association (DFG) grant BR 83576-3
The work of the author was supported by the German Research Association (DFG) grant BR 835/7-1
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Schreiber, F., Skodinis, K. (1998). NP-Completeness of Some Tree-Clustering Problems. In: Whitesides, S.H. (eds) Graph Drawing. GD 1998. Lecture Notes in Computer Science, vol 1547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37623-2_22
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