Random graph theory provides a probabilistic framework for modelling and analysing networks in which connections between entities are assigned according to specified random processes. From its origins ...

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.

As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They ...

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 ...