Dually chordal graph
In the mathematical area of graph theory, an undirected graph is dually chordal if the hypergraph of its maximal cliques is a hypertree. The name comes from the fact that a graph is chordal if and only if the hypergraph of its maximal cliques is the dual of a hypertree. Originally, these graphs were defined by maximum neighborhood orderings and have a variety of different characterizations. Unlike for chordal graphs, the property of being dually chordal is not hereditary, i.e., induced subgraphs of a dually chordal graph are not necessarily dually chordal (hereditarily dually chordal graphs are exactly the strongly chordal graphs), and a dually chordal graph is in general not a perfect graph. Dually chordal graphs appeared first under the name HT-graphs. Characterizations Dually chordal graphs are the clique graphs of chordal graphs, i.e., the intersection graphs of maximal cliques of chordal graphs. The following properties are equivalent: G has a maximum neighborhood ordering. There is a spanning tree T of G such that any maximal clique of G induces a subtree in T. The closed neighborhood hypergraph N(G) of G is a hypertree. The maximal clique hypergraph of G is a hypertree. G is the 2-section graph of