# Covering a symmetric crossing supermodular function with hyperedges of prescribed size

From Egres Open

Given a symmetric crossing supermodular function [math]p:2^V\to \mathbb{R}[/math] and positive integers [math]n_1,n_2,\dots,n_k[/math], does there exist a hypergraph *H=(V,E)* covering *p* and having exactly *k* hyperedges of sizes [math]n_1,n_2,\dots,n_k[/math]?

## Remarks

If the sizes are all equal then the problem was solved by Tamás Király ^{[1]}.