Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

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 ...

Rainbow connectivity examines how to assign colours to the edges of a graph so that every pair of vertices is joined by at least one “rainbow path”—a path in which no two edges share the same colour.

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...