Embedding Hierarchical Hypercube Networks into the Hypercube
IEEE Transactions on Parallel and Distributed Systems
The antimagicness of the Cartesian product of graphs
Theoretical Computer Science
Topics in Graph Theory: Graphs and Their Cartesian Product
Topics in Graph Theory: Graphs and Their Cartesian Product
Factorization of Cartesian products of hypergraphs
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
The Cartesian Product of Hypergraphs
Journal of Graph Theory
| Hi-index | 5.23 |
On 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.