The Domatic Partition Problem in Separable Graphs

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....

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Bibliographic Details
Published in:Mathematics (Basel) 2022-02, Vol.10 (4), p.640
Main Authors: Landete, Mercedes, Sainz-Pardo, José Luis
Format: Article
Language:English
Subjects:
Algorithms
Decomposition
decomposition algorithm
domatic number
domatic partition
Food science
Graphs
graphs with blocks
integer linear problem
Integer programming
Partitions (mathematics)
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10040640