Dually Chordal Graphs

Recently in several papers, graphs with maximum neighborhood orderings were characterized and turned out to be algorithmically useful. This paper gives a unified framework for characterizations of those graphs in terms of neighborhood and clique hypergraphs which have the Helly property and whose line graph is chordal. These graphs are dual (in the sense of hypergraphs) to chordal graphs. By using the hypergraph approach in a systematical way new results are obtained, some of the old results are generalized, and some of the proofs are simplified. Key words. graphs, hypergraphs, tree structure, hypertrees, duality, chordal graphs, clique hypergraphs, neighborhood hypergraphs, disk hypergraphs, Helly property, chordality of line graphs, maximum neighborhood orderings, linear time recognition, doubly chordal graphs, strongly chordal graphs, bipartite incidence graphs AMS subject classifications. 05C65, 05C75, 68R10 PII. S0895480193253415

• Type: Conference
• Year: 1993
• Where: WG
• Authors: Andreas Brandstädt, Feodor F. Dragan, Victor Chepoi, Vitaly I. Voloshin
• Keywords: Chordal Graphs, Clique Hypergraphs, Maximum Neighborhood Orderings, Theoretical Computer Science, WG 1993