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The dissociation number of a graph is the maximum order of a set of vertices of inducing a subgraph that is of maximum degree at most 1. Computing the dissociation number of a given graph is algorithmically hard even when restricted to subcubic bipartite graphs. For a graph with vertices, edges, components, and induced...
Recently Chen et al. [Tree domination in graphs, Ars Combin. 73 (2004) 193–203] asked for characterizations of the class of graphs and the class of regular graphs that have an induced dominating tree, i.e. for which there exists a dominating set that induces a tree.We give a somewhat negative answer to their question by proving that the corresponding decision problems are NP-complete. Furthermore,...
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