All Questions

Consider a complete graph on $n$ vertices. To each edge, $(i,j)$, we assign a weight, $W_{ij}$, which comes from some known distribution iid. Then, we ask the following question. Among all (weighted) ...

It is known that a graph $G=(V,E)$ with $n$ nodes and min cut $k$, must have at least $\frac{1}{2}nk$ edges. Are there any tighter bounds or expectations I can place on $|E|$ if I assume that $G$ ...