In this paper we introduce a general strategy for approximating the solution to minimisation problems in random regular graphs. We describe how the approach can be applied to the m...
We consider the problem of generating a random q-colouring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if for all v V the average degree of...
We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n, p) in the critical window, that is, for p = n−1 + λn−4/...
Algorithms are given for computing the number of n-element diagonal sets and the number of n-element strongly diagonal sets of binary sequences of length at most 2n - 2. The first...
We study here the spectra of random lifts of graphs. Let G be a finite connected graph, and let the infinite tree T be its universal cover space. If λ1 and ρ are the spectral ...