A new characterization of strongly chordal graphs Original Research Article

The ‘strength’ of an edge or cycle is the number of maximal complete subgraphs it is in. Strongly chordal graphs are characterized by every cycle of edges of strengths at least k with no chord of strength at least k always itself having strength at least k. Among hereditary clique-Helly graphs, this is equivalent to the subgraph of edges of strength at least k always forming a chordal graph.