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Volume 29, No 1, 2022, P. 5-17

UDC 519.8+518.25
V. V. Voroshilov
Complexity of the max cut problem with the minimal domination constraint

Abstract:
Let $G = (V,E,w)$ be a simple weighted undirected graph with nonnegative weights of its edges. Let $D$ be a minimal dominating set in $G$. Cutset induced by $D$ is a set of edges with one vertex in the set $D$ and the other in $V$ \ $D$. The weight of a cutset is the total weight of all its edges. The paper deals with the problem of finding a cutset with maximum weight among all minimal dominating sets. In particular, nonexistence of polynomial approximation algorithm with ratio better than $|V|^{-\frac{1}{2}}$ in case of $P\ne NP$ is proved.
Illustr. 3, bibliogr. 8.

Keywords: graph, cutset, dominating set, weighted graph, optimization problem, approximation.

DOI: 10.33048/daio.2022.29.706

Vladimir V. Voroshilov 1
1. Dostoevsky Omsk State University,
55a Mir Avenue, 644077 Omsk, Russia
e-mail: voroshil@gmail.com

Received February 19, 2021
Revised December 1, 2021
Accepted December 2, 2021

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