Coxeter theory investigates groups generated by reflections and the geometric structures arising from their actions, such as root systems and Dynkin diagrams. This body of work underpins vast areas of ...

Graph theory is moving from textbooks to traffic lights, powering smarter transportation networks worldwide. From retail deliveries to freight corridors and urban commuting, it helps planners cut ...

Graph labeling is a central topic in combinatorial optimisation that involves assigning numerical or categorical labels to vertices or edges of a graph subject to specific constraints. This framework ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

Researchers thought that they were five years away from solving a math riddle from the 1980's. In reality, and without knowing, they had nearly cracked the problem and had just given away much of the ...

A puzzle that has long flummoxed computers and the scientists who program them has suddenly become far more manageable. A new algorithm efficiently solves the graph isomorphism problem, computer ...