Recognizing Cartesian products in linear time

Recognizing Cartesian products in linear time

We present an algorithm that determines the prime factors of connected graphs with respect to the Cartesian product in linear time and space. This improves a result of Aurenhammeer, Hagauer, and Imrich [2], who compute the prime factors in O(m log n) time, where m denotes the number of vertices of G and n the number of edges. Our algorithm is conceptually simpler. It gains its efficiency by the...

Recognizing Cartesian graph bundles

Graph bundles generalize the notion of covering graphs and graph products. In this paper we extend some of the methods for recognizing Cartesian product graphs to graph bundles. Two main notions are used. The first one is the well-known equivalence relation δ defined on the edge-set of a graph. The second one is the concept of k-convex subgraphs. A subgraph H is k-convex in G, if for any two ve...

Recognizing Leveled-Planar Dags in Linear Time

Corners in Cartesian products

This note is an illustration of the density-increment method used in the proof of the density Hales-Jewett theorem for k = 3. (Polymath project [2]) I will repeat the argument applying it to a problem which is easier than DHJ. In the last section I will describe the proof of the density Hales-Jewett theorem for k = 3. The results stated here are direct interpretations of the project’s results, ...

Cartesian Products of Family of Real Linear Spaces

In this article we introduced the isomorphism mapping between cartesian products of family of linear spaces [4]. Those products had been formalized by two different ways, i.e., the way using the functor [:X,Y:] and ones using the functor " product ". By the same way, the isomorphism mapping was defined between Cartesian products of family of linear normed spaces also. The notation and terminolo...