Paper
Time to Cycle
Authors
Nir Lavee, Nati Linial
Abstract
Consider the random process that starts with vertices and no edges, where the edges of are added one at a time in a uniformly chosen random order . Let be the earliest time at which belongs to a cycle in this evolving random graph. By solving the appropriate graph enumeration problem we show that . This fact turns out to be an instance of a much more general phenomenon and we are able to extend this theorem to all graphs and even to every matroid.