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Reducing the Domination Number of Graphs via Edge Contractions

Authors Esther Galby, Paloma T. Lima, Bernard Ries



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Author Details

Esther Galby
  • Department of Informatics, University of Fribourg, Fribourg, Switzerland
Paloma T. Lima
  • Department of Informatics, University of Bergen, Bergen, Norway
Bernard Ries
  • Department of Informatics, University of Fribourg, Fribourg, Switzerland

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Esther Galby, Paloma T. Lima, and Bernard Ries. Reducing the Domination Number of Graphs via Edge Contractions. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 41:1-41:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.41

Abstract

In this paper, we study the following problem: given a connected graph G, can we reduce the domination number of G by at least one using k edge contractions, for some fixed integer k >= 0? We show that for k <= 2, the problem is coNP-hard. We further prove that for k=1, the problem is W[1]-hard parameterized by the size of a minimum dominating set plus the mim-width of the input graph, and that it remains NP-hard when restricted to P_9-free graphs, bipartite graphs and {C_3,...,C_{l}}-free graphs for any l >= 3. Finally, we show that for any k >= 1, the problem is polynomial-time solvable for P_5-free graphs and that it can be solved in FPT-time and XP-time when parameterized by tree-width and mim-width, respectively.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • domination number
  • blocker problem
  • graph classes

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References

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