Incidence graphs of biacyclic hypergraphs
It is known that the incidence graphs of totally balanced hypergraphs are the chordal bipartite graphs. A hypergraph is called acyclic if it is conformal and its 2-section graph is chordal. A hypergraph is called biacyclic if it and its dual are acyclic. In this paper the incidence graphs of biacyclic hypergraphs are characterized as the neighbourhood-Helly graphs whose square is chordal. Equivalently, these graphs are characterized in terms of maximum neighbourhood orderings and in terms of certain retracts with certain forbidden isometric wheels. For a more general investigation of graphs with maximum neighbourhood orderings, see \textit{A. Brandstädt}, \textit{F. F. Dragan}, \textit{V. D. Chepoi} and \textit{V. I. Voloshin} [Dually chordal graphs, Lect. Notes Comput. Sci. 790, 237-251 (1994)]. A corollary is that an irreflexive graph \(G\) is chordal bipartite if and only if every induced subgraph of \(G\) has a maximum neighborhood ordering.
scientific article; zbMATH DE number 933126
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