Linear Separation of Connected Dominating Sets in Graphs
نویسندگان
چکیده
A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. We introduce and study the class of connected-domishold graphs, which are graphs that admit non-negative real weights associated to their vertices such that a set of vertices is a connected dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. We show that these graphs form a non-hereditary class of graphs properly containing two well known classes of chordal graphs: block graphs and trivially perfect graphs. We characterize, in several ways, the graphs every induced subgraph of which is connecteddomishold: in terms of forbidden induced subgraphs, in terms of 2-asummability of certain derived Boolean functions, and in terms of the dually Sperner property of certain de-
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