Connected domination and dominating clique in trapezoid graphs
The class of trapezoid graphs is defined as the intersection graphs of a collection of trapezoids. A set of vertices that dominates the graph and induces a connected graph is a connected dominating set. The smallest set is called the connected domination number for the graph. It is known that this problem is NP-hard. The author develops an \(O(n)\) algorithm for finding a minimum connected dominating set in a trapezoid graph. If a trapezoid graph has a dominating clique, the author develops an \(O(m+n)\) algorithm for finding such a clique. This algorithm depends on the fact that if such a clique exists, then it has cardinality at most four.
scientific article; zbMATH DE number 1395006