A 2-Isomorphism Theorem for Hypergraphs

Abstract

One can associate a polymatroid with a hypergraph that naturally generalises the cycle matroid of a graph. Whitney's 2-isomorphism theorem characterises when two graphs have isomorphic cycle matroids. In this paper Whitney's theorem is generalised to hypergraphs and polymatroids by characterising when two hypergraphs have isomorphic associated polymatroids.