eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-11-28
21:1
21:14
10.4230/LIPIcs.ISAAC.2019.21
article
Blocking Dominating Sets for H-Free Graphs via Edge Contractions
Galby, Esther
1
Lima, Paloma T.
2
Ries, Bernard
1
Department of Informatics, University of Fribourg, Fribourg, Switzerland
Department of Informatics, University of Bergen, Bergen, Norway
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol149-isaac2019/LIPIcs.ISAAC.2019.21/LIPIcs.ISAAC.2019.21.pdf
domination number
blocker problem
H-free graphs