Edge colouring is a fundamental concept in graph theory whereby colours are assigned to the edges of a graph such that no two adjacent edges share the same colour. This process is central to numerous ...

Edge-Colored Graph Theory is a vibrant area within combinatorics that extends the classical study of graphs by assigning colours to edges. This paradigm not only uncovers subtle structural properties ...

Korean research institute Kaist has found a way to develop a one trillion edge graph algorithm on a single computer without storing the graph in the main memory or on disc. ‘Develop’ is the important ...

Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

Graphs are widely used to represent a wide variety of systems, ranging from the relationships between users of a social network to the payments among a network of bank accounts, and graph algorithms ...

A research team has developed a new technology that enables to process a large-scale graph algorithm without storing the graph in the main memory or on disks. A KAIST research team has developed a new ...

In this paper, we introduce a new simple but powerful general technique for the study of edge- and vertex-reinforced processes with super-linear reinforcement, based on the use of order statistics for ...

Forbes contributors publish independent expert analyses and insights. I write about the broad intersection of data and society. One of the most powerful ways through which we convey the results of ...