Upper Domination: Complexity and Approximation

  title={Upper Domination: Complexity and Approximation},
  author={Cristina Bazgan and Ljiljana Brankovic and Katrin Casel and Henning Fernau and Klaus Jansen and Kim-Manuel Klein and Michael Lampis and Mathieu Liedloff and J{\'e}r{\^o}me Monnot and Vangelis Th. Paschos},
We consider Upper Domination, the problem of finding a maximum cardinality minimal dominating set in a graph. We show that this problem does not admit an \(n^{1-\epsilon }\) approximation for any \(\epsilon >0\), making it significantly harder than Dominating Set, while it remains hard even on severely restricted special cases, such as cubic graphs (APX-hard), and planar subcubic graphs (NP-hard). We complement our negative results by showing that the problem admits an \(O(\varDelta… 

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