Signatures of Extremal 2-Unifrom Hypergraphs

Goltsova, T. Yu.; Егорова, Е. К.; Mokryakov, A. V.; Цурков, В. И.

doi:10.1134/s1064230721060095

Cited by 3 publications

(6 citation statements)

References 6 publications

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“…In [39], the «signature» for EUH 2 n is presented. In [56], an extension of the notion of signature is presented: a second-order signature, or vector of signatures, for EUH 3 n .…”

Section: Definitionmentioning

confidence: 99%

“…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%

“…In [39], we describe another approach to the representation of an extremal 2-uniform hypergraph: the signature. It is given as a non-negative integer having exactly 1 digit less than the vertices in the hypergraph in binary representation.…”

Section: Introductionmentioning

confidence: 99%

“…In [56,57], a new representation is given for an extremal 3-uniform hypergraph, and operations under signatures are described.…”

Section: Introductionmentioning

confidence: 99%

“…The structure of the base makes it quite easy to enumerate all its possible variants but makes it almost a simple enumeration. Thanks to the second-order signature representation, which appeared in the works of [56,57], as well as operations on these representations of extreme 3 uniform hypergraphs, we are able to propose a new, more efficient algorithm for calculating the cardinality of a set.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Egorova,

Leonov,

Mokryakov

et al. 2024

Axioms

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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.

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“…In [39], the «signature» for EUH 2 n is presented. In [56], an extension of the notion of signature is presented: a second-order signature, or vector of signatures, for EUH 3 n .…”

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In [56,57], a new representation is given for an extremal 3-uniform hypergraph, and operations under signatures are described.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Egorova,

Leonov,

Mokryakov

et al. 2024

Axioms

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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.

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The Algebra of Signatures for Extreme Two-Uniform Hypergraphs

Egorova,

Mokryakov,

Tsurkov

2023

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In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal two-uniform hypergraph itself. However, for the signature, although various algorithms have been derived for transforming it into other object-characteristics such as the base, the adjacency matrix, and the vector of vertex degrees, no isolated signature union and intersection apparatus has been constructed. This allows us to build efficient algorithms based on signatures, the most compact representation of extremal two-uniform hypergraphs. The nature of the algebraic construction that can be built on a set of signatures using union and intersection operations has also been defined. It is proved that an algebra on a set of signatures with either the union or intersection operation forms a monoid; if the algebra is defined on a set of signatures with both union and intersection operations, it forms a distributive lattice.

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Signatures of Extremal 2-Unifrom Hypergraphs

Cited by 3 publications

References 6 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

The Algebra of Signatures for Extreme Two-Uniform Hypergraphs

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