Hereditary Classes of Line Graphs

We investigate the connections between families of graphs closed under (induced) subgraphs and their forbidden (induced) subgraph characterizations. In particular, we discuss going from a forbidden subgraph characterization of a family \(\mathbb{P}\) to a forbidden induced subgraph characterization of the family of line graphs of members of \(\mathbb{P}\) in the most general case. The inverse problem is considered too.