The k -core of a graph is the largest subgraph with minimum degree at least k . For the Erdős-Rényi random graph G(n,m) on n vertices, with m edges, it is known that a giant 2-core grows simultaneously with a giant component, that is when m is close to n/2 . We show that for k ≥ 3 , with high probability, a giant k -core appears suddenly when m reaches ckn… (More)