Li, R and Miklós, István (2025) Dense, irregular, yet always-graphic 3-uniform hypergraph degree sequences. DISCRETE MATHEMATICS, 348 (9). ISSN 0012-365X 10.1016/j.disc.2025.114498

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Abstract

A 3-uniform hypergraph is a generalization of a simple graph where each hyperedge is a subset of exactly three vertices. The degree of a vertex in a hypergraph is the number of hyperedges incident with it. The degree sequence of a hypergraph is the sequence of the degrees of its vertices. The degree sequence problem for 3-uniform hypergraphs asks whether a 3-uniform hypergraph with a given degree sequence exists. Such a hypergraph is called a realization. Recently, Deza et al. proved that this problem is NP-complete. Although some special cases are simple, polynomial-time algorithms are only known for highly restricted degree sequences. The main result of our research is the following: if all degrees in a sequence D of length n are between [Formula presented]+O(n) and [Formula presented]−O(n), the number of vertices is at least 45, and the degree sum is divisible by 3, then D has a 3-uniform hypergraph realization. Our proof is constructive, providing a polynomial-time algorithm for constructing such a hypergraph. To our knowledge, this is the first polynomial-time algorithm to construct a 3-uniform hypergraph realization of a highly irregular and dense degree sequence. © 2025 The Authors

Item Type:	Article
Uncontrolled Keywords:	3-uniform hypergraphs; Degree sequence problems; Dense, irregular degree sequences;
Subjects:	Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions:	Informatics Laboratory
SWORD Depositor:	MTMT Injector
Depositing User:	MTMT Injector
Date Deposited:	12 Apr 2025 07:13
Last Modified:	12 Apr 2025 07:13
URI:	https://eprints.sztaki.hu/id/eprint/10899

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