The complexity of connected dominating sets and total dominating sets with specified induced subgraphs

Authors:
Oliver Schaudt;Rainer Schrader
Affiliations:
Institut für Informatik, Arbeitsgruppe Faigle/Schrader, Universität zu Köln, Weyertal 80, 50931 Cologne, Germany;Institut für Informatik, Arbeitsgruppe Faigle/Schrader, Universität zu Köln, Weyertal 80, 50931 Cologne, Germany
Venue:
Information Processing Letters
Year:
2012

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Abstract

Given a graph class G, it is natural to ask (i) whether a given graph G has a connected or a total dominating set whose induced subgraph is a member of G and (ii) whether G has such a set of cardinality at most a given threshold. We give sufficient conditions on G under which these two problems are NP-hard. This condition is fulfilled in a wide variety of classes of graphs.