Recognizing Cartesian products in linear time

TL;DR: The literature on hypergraph products is surveyed with an emphasis on comparing the alternative generalizations of graph products and the relationships among them, and the so-called 2-sections and L2-sections are considered.

TL;DR: In this article, the authors propose a deterministic graph-minor embedding method for the Cartesian product of two complete graphs, a regular structure that occurs in many problems.

TL;DR: In this paper, the authors introduced simplified definitions of Cartesian skeletons for the direct and strong products, and provided new, fast and transparent algorithms for their construction, which improved the complexity of the prime factorization of the direct product with respect to the strong product.

TL;DR: This paper presents an algorithm for drawing graph products and the aesthetic criterion graph product's drawings are subject to, and shows that the popular High-Dimensional Embedder approach applied to cartesian products already respects this aestetic criterion, but has disadvantages.

TL;DR: In this article, the authors introduce fundamental concepts and colouring problems in graph analysis, including thickness, genus of graph, isomorphism, and metric questions, with given properties.

TL;DR: This hierarchy starts with the isometric representation, includes the 2-isometric represnetation, and ends with the cartesian prime factorization, and it is shown that all three representations can be obtained in O(nm) time using O(m) space, for graphs with n vertices and m edges.

TL;DR: A polynomial-time algorithm for deciding whether a given connected graph is a non-trivial Cartesian product of graphs, which entails first representing the graph as an isometric subgraph of a Cartesian products, then finding a suitable partition of the factors.