The stripping process can be slow: Part I

Given an integer k, we consider the parallel k-stripping process applied to a hypergraph H: removing all vertices with degree less than k in each iteration until reaching the k-core of H. Take H as Hr(n,m): a random r-uniform hypergraph on n vertices and m hyperedges with the uniform distribution. Fixing k,r2 with (k,r)(2,2), it has previously been proved that there is a constant cr,k such that for all m=cn with constant ccr,k, with high probability, the parallel k-stripping process takes O(log?n) iterations. In this paper, we investigate the critical case when c=cr,k+o(1). We show that the number of iterations that the process takes can go up to some power of n, as long as c approaches cr,k sufficiently fast. A second result we show involves the depth of a non-k-core vertex v: the minimum number of steps required to delete v from Hr(n,m) where in each step one vertex with degree less than k is removed. We will prove lower and upper bounds on the maximum depth over all non-k-core vertices.