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Partitioning trees: Matching, domination, and maximum diameter

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Abstract

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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Authors and Affiliations

  1. Department of Computer and Information Science, University of Oregon, 97403, Eugene, Oregon

    Arthur Parley, Stephen Hedetniemi & Andrzej Proskurowski

Authors
  1. Arthur Parley
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  2. Stephen Hedetniemi
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  3. Andrzej Proskurowski
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Additional information

Research supported in part by the National Science Foundation under Grant ENG 7902960.

Research supported in part by the National Science Foundation under Grant STI 7902960.

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Parley, A., Hedetniemi, S. & Proskurowski, A. Partitioning trees: Matching, domination, and maximum diameter. International Journal of Computer and Information Sciences 10, 55–61 (1981). https://doi.org/10.1007/BF00978378

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  • DOI: https://doi.org/10.1007/BF00978378

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