Properties of Unique Degree Sequences of 3-Uniform Hypergraphs

In 2018 Deza et al. proved the NP-completeness of deciding wether there exists a 3-uniform hypergraph compatible with given degree sequence. A well known result Erdos and Gallai (1960) shows that same problem related to graphs can be solved in polynomial time. So, it becomes relevant detect classes uniform hypergraphs are reconstructible particular, our study concerns defined proof Those constructed starting from non-increasing sequence s integers have very interesting properties. they unique, i.e., do not exist two non isomorphic having \(d_s\). This property makes us conjecture reconstruction these their sequences done we first generalize computation \(d_s\) by al., show uniqueness. We proceed defining equivalence integer determining define (minimal) representative. Then, find asymptotic growth rate maximal element representatives terms length sequence, aim generating then reconstructing them. Finally, an example unique similar those does admit s. The existence this extended algorithm for include much wider class hypergraphs. Further studies could also strategies identification new