On the Reconstruction of 3-Uniform Hypergraphs from Step-Two Degree Sequences

A nonnegative integer sequence is k-graphic if it the degree of a k-uniform simple hypergraph. The problem deciding whether given \(\pi \) admits 3-uniform hypergraph has recently been proved to be NP-complete, after long years research. Thus, helpful find which classes instances are polynomially solvable in order restrict NP-hard core and design algorithms for real-life applications. Several necessary few sufficient conditions k-graphic, with \(k\ge 3\), appear literature. Frosini et al. defined polynomial time algorithm reconstruct hypergraphs having regular or almost sequences. Our study fits this research line defining some step-two sequences, i.e., =(d,\dots ,d,d-2,\dots ,d-2)\). results likely easily generalized \(k \ge 4\) other families similar