International audienceOn the one hand Cartesian products of graphs have been extensively studied since the 1960s. On the other hand hypergraphs are a well-known and useful generalization of graphs. In this article, we present an algorithm able to factorize into its prime factors any bounded-rank and bounded-degree hypergraph in O(nm), where n is the number of vertices and m is the number of hyperedges of the hypergraph. First the algorithm applies a graph factorization algorithm to the 2-section of the hypergraph. Then the 2-section factorization is used to build the factorization of the hypergraph via the factorization of its L2-section. The L2-section is a recently introduced way to interpret a hypergraph as a labeled-graph. The graph factorization algorithm used in this article is due to Imrich and Peterin and is linear in time and space. Nevertheless any other such algorithm could be extended to a hypergraph factorization algorithm similar to the one presented here

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.

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