A new characterization of strongly chordal graphs
Define the strength of a set of edges as the number of inclusion-maximal complete subgraphs that contain it. The main result is that a graph is strongly chordal if and only if, for every \(k\geq 1\), every cycle of edges of strength at least \(k\) with no chord of strength at least \(k\) itself has strength at least \(k\). This approach being applied to the hereditary clique-Helly graphs provides that such a graph is strongly chordal if and only if, for every \(k\), the edges of strength at least \(k\) form a chordal graph.
scientific article; zbMATH DE number 1334694