Abstract
We study a new version of the domination problem in which the dominating set is required to be a clique. The minimum dominating clique problem is NP-complete for split graphs and, hence, for chordal graphs. We show that for two other important subclasses of chordal graphs the problem is solvable efficiently. We present an O( m · log n) algorithm for strongly chordal graphs and an O( n 4) algorithm for undirected path graphs.
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