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, ...

Properties of the colour-distribution in edge-colourings of graphs are examined. The results are applied in generalizing two theorems of Vizing and in proving the following for m = 5 and 7: If G is ...

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 ...

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 ...

Graph databases offer a more efficient way to model relationships and networks than relational (SQL) databases or other kinds of NoSQL databases (document, wide column, and so on). Lately many ...

The intersection of large language models and graph databases is one that’s rich with possibilities. The folks at property graph database maker Neo4j today took a first step in realizing those ...

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 ...