Forbidden configurations in intersection graphs of r-graphs

Abstract

An r-graph or r-uniform hypergraph is a finite family of subsets of a set X in which each subset has cardinality r. The intersection graph of an r-graph H is the graph whose nodes are the sets of H with two nodes adjacent whenever the corresponding sets have a nonempty intersection. We show that a finite forbidden graph characterization of the intersection graphs of r-graphs is impossible by constructing two infinite, irreducible classes of forbidden subgraphs.