A unified approach to domination problems on interval graphs (Q1111566)

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.