A graph is chordal if and only if every cycle either has a chord or is a triangle. If an edge (or triangle) is defined to be a strength- edge (or triangle) whenever it is in at least maximum cliques, then a graph is strongly chordal if and only if, for every , every cycle of strength- edges either has a strength- chord or is a strength- triangle. Dual-chordal graphs have been defined so as to be the natural cycle/cutset duals of chordal graphs. A carefully crafted notion of dual strength allows a characterization of strongly dual-chordal graphs that is parallel to the above. This leads to a complete list of all -connected strongly dual-chordal graphs.
