Dualizing chordal graphs (Q1869220)

This paper studies dual-chordal graphs, that is, graphs that are dual to chordal graphs with regard to cycle/cutset duality. A characteristic of such graphs is that every cutset with at least four edges is accompanied by a certain kind of edge, a ``cut-chord.'' One result allows us to recognize dual-chordal graphs by simply looking at cubic graphs. We have a strongly dual-chordal graph if every cutset with at least five edges has a ``strong'' cut-chord. Among these, the planar ones turn out to be triangular prisms with parallel ``struts'' or just \(K_4\).