Cartesian product of hypergraphs: properties and algorithms

TL;DR

This paper explores properties and algorithms related to the Cartesian product of hypergraphs, extending classical graph results to hypergraphs and focusing on coloring and factorization methods.

Contribution

It introduces new properties and algorithms for hypergraph Cartesian products, including extending prime factorization to connected conformal hypergraphs.

Findings

Extended prime factorization algorithm to hypergraphs

Developed new coloring properties for hypergraph products

Provided algorithms for hypergraph Cartesian product analysis

Abstract

Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs.