On the concentration of the independence numbers of random hypergraphs

Денисов, Илья Олегович; Denisov, Ilya Olegovich; Шабанов, Дмитрий Александрович; Шабанов, Д. А.

doi:10.4213/dm1676

Cited by 5 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hypergraph models are widely used in solving a number of problems: extreme problems [27,28], covers [29,30], coloring [21,22], pathfinding [31][32][33], the internal structure of a hypergraph-its topology [20,34], hypergraph storage [35][36][37][38][39], and structures of random hypergraphs [40,41].…”

Section: Introductionmentioning

confidence: 99%

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

Egorova,

Leonov,

Mokryakov

et al. 2024

Axioms

View full text Add to dashboard Cite

This paper continues the study of second-order signature properties—the characterization of the extreme 3-uniform hypergraph. Previously, bases were used to count extreme 3-uniform hypergraphs. However, the algorithm using this mechanism is extremely labor-intensive. The structure of the signature allows us to use it as a more efficient basis for the same problem. Here, we establish the nature of the mutual correspondence between the kind of second-order signature and extreme hypergraphs, and we present a new algorithm to find the power of the set of extreme 3-uniform hypergraphs through the set of their characteristic-signatures. New results obtained with the proposed tool are also presented.

show abstract

Section: Introductionmentioning

confidence: 99%

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

Egorova,

Leonov,

Mokryakov

et al. 2024

Axioms

View full text Add to dashboard Cite

show abstract

Combination of Bases and an Evaluation of the Set of Extremal 3-Uniform Hypergraphs

Beretskii,

Egorova,

Mokryakov

et al. 2023

J. Comput. Syst. Sci. Int.

View full text Add to dashboard Cite

First and Second Order Signatures of Extreme Uniform Hypergraphs and Their Relationship with Vectors of the Vertex Degrees

Goltsova,

Egorova,

Leonov

et al. 2023

Teoriâ i sistemy upravleniâ

View full text Add to dashboard Cite

The adjacency matrices of extremal 3-uniform hypergraphs occupy a significant amount of computer memory. The solution of two problems is considered: to propose an efficient way of representing and storing such matrices and to find fast algorithms that allow us to operate just with vectors of the vertex degrees and signatures (characteristics of adjacency matrices), without using adjacency matrices in memory. As part of the first task, a second-order signature that uniquely defines an extremal 3-uniform hypergraph without using its adjacency matrix is described. A mechanism for compressing the second-order signature is also proposed, which contributes to greater storage efficiency. For the second problem, a number of algorithms are presented to describe the relationship between the vector of the vertex degrees and signatures of both the first and second orders. In addition, it is shown that an arbitrary second-order signature constructed under a number of constraints always has an extremal 3-uniform hypergraph corresponding to it.

show abstract

On the concentration of the independence numbers of random hypergraphs

Cited by 5 publications

References 13 publications

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

Combination of Bases and an Evaluation of the Set of Extremal 3-Uniform Hypergraphs

First and Second Order Signatures of Extreme Uniform Hypergraphs and Their Relationship with Vectors of the Vertex Degrees

Contact Info

Product

Resources

About