DOUBLY CHORDAL GRAPHS, STEINER TREES, AND CONNECTED DOMINATION

A new class of chordal graphs, containing the class of strongly chordal graphs, is introduced. It is shown that these graphs, called doubly chordal graphs, are related to acyclic hypergraphs and are recognizable in polynomial time. Furthermore, after proving that the Steiner tree and the connected domination problems are polynomially solvable for doubly chordal graphs, it is shown that both problems are NP-hard for a class of chordal graphs (called Helly chordal graphs) containing the class of doubly chordal graphs.