Some NP-complete problems for hypergraph degree sequences

A k-hypergraph G has vertex-set V(G) and edge-set E(G) consisting of k-subsets of V(G). If uε{lunate}V(G), then those edges of G containing u define a (k-1)-hypergraph G_u. We say G subsumes the (k-1)-hypergraphs {G_u|;uε{lunate}V(G)}. Given n graphs (i.e., 2-hyperegraphs) g₁, g₂, ... g_n, is there a 3-hypergraph G such that the subsumed graphs G_i{succeeds or equal to}g_i, for i=1, 2, ..., n? Given only the degree sequences of n graphs g₁, g₂, ..., g_n, is there a 3-hypergraph G whose subsumed graphs G₁, G₂, ..., G_n have the same degree sequences? We consider 3-hypergraphs with and without repeated edges. We prove these problems NP-complete. We indicate their relation to some well-known problems. The corresponding problems for 2-hypergraphs have simple polynomial solutions.