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 ...

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 ...

In the fall of 1972, Vance Faber was a new professor at the University of Colorado. When two influential mathematicians, Paul Erdős and László Lovász, came for a visit, Faber decided to host a tea ...

Efficiently and quickly chewing through one trillion edges of a complex graph is no longer in itself a standalone achievement, but doing so on a single node, albeit with some acceleration and ...

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible. A paper posted online last month has disproved a ...