Develop dichotomy theorems under alternative degree-sequence parametrizations

Investigate whether dichotomy theorems analogous to the sparse t-uniform hypergraphicality dichotomy can be established using alternative parametrizations, such as the maximum degree together with the sum of the degrees.

Background

The paper's main theorem classifies sparse t-uniform hypergraphical degree sequences using the minimum- and maximum-degree exponents. It explicitly raises the unresolved question of whether comparable computational phase transitions can be obtained when degree sequences are instead parameterized by other aggregate quantities, particularly the maximum degree and total degree sum.