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Blocking Dominating Sets for H-Free 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. Blocking Dominating Sets for H-Free Graphs via Edge Contractions. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ISAAC.2019.21

Abstract

In this paper, we consider the following problem: given a connected graph G, can we reduce the domination number of G by one by using only one edge contraction? We show that the problem is NP-hard when restricted to {P_6,P_4+P_2}-free graphs and that it is coNP-hard when restricted to subcubic claw-free graphs and 2P_3-free graphs. As a consequence, we are able to establish a complexity dichotomy for the problem on H-free graphs when H is connected.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • domination number
  • blocker problem
  • H-free graphs

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