Random lifts of graphs

Alon Amit, Nathan Linial, Jirí Matousek, Eyal Rozenman

Abstract: We describe here a simple probabilistic model for graphs that are lifts of a fixed base graph G, i.e., those graphs from which there is a covering man onto G. Our aim is to investigate the properties of typical graphs in this class. In particular, we show that almost every lift of G is δ(G)-connected where δ(G) is the minimal degree of G. We calculate the typical edge expansion of lifts of the bouquet Bd and