Intersection Multigraphs of Uniform Hypergraphs

Abstract.

The intersection multigraph of a simple hypergraph H=(V, {X _i /i∈I}) has {x _i /i∈I} as vertex set. Two distinct vertices x _i ≠x _j are joined by |X _i ∩X _j | parallel edges. It is shown how to recognize intersection multigraphs of 3-uniform, 3-conformal hypergraphs in polynomial time and reveal the (essentially unique) root hypergraph. For integers k≥4, intersection multigraphs of k-uniform, k-conformal hypergraphs with one additional property can be recognized.