Cutoff for random lifts of weighted graphs

Random Lifts of Graphs III :

Hamilton cycles in random lifts of graphs

An n-lift of a graph K, is a graph with vertex set V (K)× [n] and for each edge (i, j) ∈ E(K) there is a perfect matching between {i} × [n] and {j} × [n]. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that there are constants h1, h2 such that if h ≥ h1 then a random n-lift of the complete graph Kh is hamiltonian whp and if ...

Random Lifts of Graphs are Highly Connected

In this note we study asymptotic properties of random lifts of graphs introduced by Amit and Linial as a new model of random graphs. Given a base graph G and an integer n, a random lift of G is obtained by replacing each vertex of G by a set of n vertices, and joining these sets by random matchings whenever the corresponding vertices of G are adjacent. In this paper we study connectivity proper...

δ-Connectivity in Random Lifts of Graphs

Amit and Linial have shown that a random lift of a connected graph with minimum degree δ > 3 is asymptotically almost surely (a.a.s.) δ-connected and mentioned the problem of estimating this probability as a function of the degree of the lift. Using a connection between a random n-lift of a graph and a randomly generated subgroup of the symmetric group on n-elements, we show that this probabili...

Random Lifts of Graphs II: Edge Expansion