Partitioning trees: Matching, domination, and maximum diameter

@article{Farley1981PartitioningTM,
  title={Partitioning trees: Matching, domination, and maximum diameter},
  author={Arthur M. Farley and Stephen T. Hedetniemi and Andrzej Proskurowski},
  journal={International Journal of Computer & Information Sciences},
  year={1981},
  volume={10},
  pages={55-61}
}
A matching and a dominating set in a graph G are related in that they determine diameter-bounded subtree partitions of G. For a maximum matching and a minimum dominating set, the associate partitions have the fewest numbers of trees. The problem of determining a minimum dominating set in an arbitrary graph G is known to be NP-complete. In this paper we present a linear algorithm for partitioning an arbitrary tree into a minimum number of subtrees, each having a diameter at mostk, for a givenk. 

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