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

Author:

Egorova Evgeniya1ORCID,Leonov Vladislav1,Mokryakov Aleksey2ORCID,Tsurkov Vladimir1ORCID

Affiliation:

1. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, 119333 Moscow, Russia

2. Institute of Information Technology and Digital Transformation, Kosygin Russian State University (Technologies. Design. Art.), 119071 Moscow, Russia

Abstract

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.

Publisher

MDPI AG

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