Dismantling Sparse Random Graphs

Abstract

We consider the number of vertices that must be removed from a graphGin order that the remaining subgraph have no component with more thankvertices. Our principal observation is that, ifGis a sparse random graph or a random regular graph onnvertices withn→ ∞, then the number in question is essentially the same for all values ofkthat satisfy bothk→ ∞ andk=o(n).