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 ...

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 ...

Discrete structures are omnipresent in mathematics, computer science, statistical physics, optimisation and models of natural phenomena. For instance, complex random graphs serve as a model for social ...

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. It started with a bet. In the late 1980s, at a ...