k-cuts on a Path

Abstract

We define the (random)-cut number of a rooted graph to model the difficulty of the destruction of a resilient network. The process is as the cut model of Meir and Moon [14] except now a node must be cut times before it is destroyed. The first order terms of the expectation and variance of, the -cut number of a path of length, are proved. We also show that, after rescaling, converges in distribution to a limit, which has a complicated representation. The paper then briefly discusses the -cut number of general graphs. We conclude by some analytic results which may be of interest.