2 problems

Let $(G_n)$ be a sequence of $r=r(n)$-regular bipartite graphs with $n+n$ vertices. Give the edges independent exponential random weights, and let $C_n$ denote the minimum weight o…

Let $K_{n,n}$ be the complete bipartite graph with $n$ vertices on each side. A fractional bipartite matching is a collection of edge probabilities $x=(x_{uv})$ satisfying the vert…