Multi-intersection graphs Original Research Article

Let P=P1 be a hereditary class of intersection graphs. For m⩾2 denote by Pm the extension of P by admitting up to m copies for any subset (corresponding to a vertex of a graph). Clearly, Pm⊆Pm+1 for all m⩾1. Put P∗=⋃Pm over all m⩾1. We introduce a method for constructing forbidden induced subgraphs (FIS) for Pm (m⩾2) and P∗ provided that the FIS characterization for P1 is known. We apply the method to line graphs of multigraphs with/without bounded edge multiplicities.