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 ...

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 ...

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, ...

ABSTRACT. The goal of this paper is to study the structure of the minimal free resolutions associated to a class of squarefree monomial ideals by using the one-to-one correspondence between squarefree ...

Graph databases are gaining attention as enterprises work on their next-generation artificial intelligence (AI) applications. While still a bit of an outlier, graph-oriented databases continue to find ...

Another day, another graph funding round. Last week it was TigerGraph, this week it's Katana Graph. Katana Graph, a high-performance scale-out graph processing, AI, and analytics company, announced it ...

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 ...

The founding team behind The Graph debuts a new platform to unify payments, policies, and visibility for autonomous agents.

As the end of Web 2.0 draws closer, plans are in the works to build the next version of the internet, which as you may know by now, is Web 3.0. While this will herald the transition from a centralized ...

Last fall, the folks in Facebook’s engineering team talked about how they employed the Apache Giraph engine to build a graph on its Hadoop platform that can host more than a trillion edges. While the ...