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A unified approach to domination problems on interval graphs. (English) Zbl 0658.05040
A subset D of the vertex set V(G) of a graph G is called dominating (or total dominating) in G, if for each vertex $$x\in V(G)-D$$ (or for each vertex $$x\in V(G)$$ respectively) there exists a vertex $$y\in D$$ adjacent to x. A dominating set of G which induces a connected subgraph of G is called connected. Also independent dominating sets are considered. The mentioned concepts are studied for interval graphs, i.e. intersection graphs of families of intervals on a real line. Some recurrence relations for various types of dominating sets in interval graphs are stated. These relations lead to linear-time algorithms for the weighted version of the various dominating problems in a unified way.