Abstract
Let \( G=(V,E,w) \) be a simple weighted undirected graph with nonnegative edge weights. Let \( D \) be a minimal dominating set in \( G \). The cutset induced by \( D \) is the set of edges with one vertex in the set \( D \) and the other in \( V\setminus D \). The weight of the cutset is the total weight of all its edges. The paper deals with the problem of finding a cutset with the maximum weight among all minimal dominating sets. In particular, the nonexistence of a polynomial approximation algorithm with a ratio better than \( |V|^{-\frac {1}{2}} \) in the case of \( \text {P}\ne \text {NP} \) is proved.
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Translated by V. Potapchouck
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Voroshilov, V.V. Complexity of the max cut Problem with the Minimal Domination Constraint. J. Appl. Ind. Math. 16, 168–174 (2022). https://doi.org/10.1134/S1990478922010161
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DOI: https://doi.org/10.1134/S1990478922010161