Polynomial reconstruction problem for hypergraphs

We show that, in general, the characteristic polynomial of a hypergraph is not determined by its "polynomial deck", the multiset of characteristic polynomials of its vertex-deleted subgraphs, thus settling the "polynomial reconstruction problem" for hypergraphs in the negative. The proof proceeds by showing that a construction due to Kocay of an infinite family of pairs of 3-uniform hypergraphs which are nonisomorphic but share the same hypergraph deck, in fact, have different characteristic polynomials. The question remains unresolved for ordinary graphs. (c) 2024 Elsevier Inc. All rights reserved.