A k-separated matching in a graph is a set of edges at distance at least k from one another (hence, for instance, a 1-separated matching is just a matching in the classical sense)...
We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and deri...
Let G be a d-regular graph with girth g, and let α be the independence number of G. We show that α(G) ≥ 1 2 1 − (d − 1)−2/(d−2) − (g) n where (g) → 0 as g → ∞,...