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 → ∞,...
: Suppose that independent U 0 1 weights are assigned to the d 2 n2 edges of the complete d-partite graph with n vertices in each of the d = maximal independent sets. Then the expe...
A random geometric graph G(n, r) is a graph resulting from placing n points uniformly at random on the unit area disk, and connecting two points iff their Euclidean distance is at ...
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...
We consider the classical rumor spreading problem, where a piece of information must be disseminated from a single node to all n nodes of a given network. We devise two simple pus...
George Giakkoupis, Thomas Sauerwald, He Sun, Phili...