# A Survey on Hypergraph Products (Erratum)

## TL;DR

This survey reviews various hypergraph products, comparing their properties and relationships, with emphasis on generalizations of graph products, and discusses their effects on hypergraph invariants across finite, infinite, and directed cases.

## Contribution

It provides a comprehensive comparison of hypergraph product variants, highlighting their interrelations and implications for hypergraph invariants, including less-studied infinite and directed hypergraphs.

## Key findings

- Most hypergraph products generalize standard graph products.
- The square product is a unique variant not fitting the generalization pattern.
- Hypergraph invariants propagate differently under various hypergraph products.

## Abstract

A surprising diversity of different products of hypergraphs have been discussed in the literature. Most of the hypergraph products can be viewed as generalizations of one of the four standard graph products. The most widely studied variant, the so-called square product, does not have this property, however. Here we survey the literature on hypergraph products with an emphasis on comparing the alternative generalizations of graph products and the relationships among them. In this context the so-called 2-sections and L2-sections are considered. These constructions are closely linked to related colored graph structures that seem to be a useful tool for the prime factor decompositions w.r.t.\ specific hypergraph products. We summarize the current knowledge on the propagation of hypergraph invariants under the different hypergraph multiplications. While the overwhelming majority of the material concerns finite (undirected) hypergraphs, the survey also covers a summary of the few results on products of infinite and directed hypergraphs.