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- W3161036109 abstract "A nonnegative integer sequence is k-graphic if it is the degree sequence of a k-uniform simple hypergraph. The problem of deciding whether a given sequence (pi ) admits a 3-uniform simple hypergraph has recently been proved to be NP-complete, after long years of research. Thus, it is helpful to find which classes of instances are polynomially solvable in order to restrict the NP-hard core of the problem and design algorithms for real-life applications. Several necessary and few sufficient conditions for (pi ) to be k-graphic, with (kge 3), appear in the literature. Frosini et al. defined a polynomial time algorithm to reconstruct k-uniform hypergraphs having regular or almost regular degree sequences. Our study fits in this research line defining some conditions and a polynomial time algorithm to reconstruct 3-uniform hypergraphs having step-two degree sequences, i.e., (pi =(d,dots ,d,d-2,dots ,d-2)). Our results are likely to be easily generalized to (k ge 4) and to other families of similar degree sequences." @default.
- W3161036109 created "2021-05-24" @default.
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- W3161036109 date "2021-01-01" @default.
- W3161036109 modified "2023-09-25" @default.
- W3161036109 title "On the Reconstruction of 3-Uniform Hypergraphs from Step-Two Degree Sequences" @default.
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- W3161036109 doi "https://doi.org/10.1007/978-3-030-76657-3_24" @default.
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