Power of k choices and rainbow spanning trees in random graphs

Deepak Bal, Patrick Bennett, Alan Frieze, Pawee, Praa Lat
We consider the Erd˝ os-Rényi random graph process, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new edge chosen uniformly at random from the set of missing edges. Let G(n, m) be a graph with m edges obtained after m steps of this process. Each edge e i (i = 1, 2, .