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The Domatic Partition Problem in Separable Graphs

Author

Listed:
  • Mercedes Landete

    (Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202 Elche, Spain)

  • José Luis Sainz-Pardo

    (Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202 Elche, Spain)

Abstract

The domatic partition problem consists of partitioning a given graph into a maximum number of disjoint dominating sets. This problem is related with the domatic number problem, which consists of quantifying this maximum number of disjoint dominating sets. Both problems were proved to be NP-complete. In this paper, we present a decomposition algorithm for finding a domatic partition on separable graphs, that is, on graphs with blocks, and as a consequence, its domatic number, highly reducing the computational complexity. Computational results illustrate the benefits of the block decomposition algorithm.

Suggested Citation

  • Mercedes Landete & José Luis Sainz-Pardo, 2022. "The Domatic Partition Problem in Separable Graphs," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:640-:d:753125
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    References listed on IDEAS

    as
    1. Mercedes Landete & Alfredo Marín & José Luis Sainz-Pardo, 2017. "Decomposition methods based on articulation vertices for degree-dependent spanning tree problems," Computational Optimization and Applications, Springer, vol. 68(3), pages 749-773, December.
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