An Optimal Algorithm for Finding Frieze-Kannan Regular Partitions.

In this paper we prove that two local conditions involving the degrees and co-degrees in a graph can be used to determine whether a given vertex partition is Frieze-Kannan regular. With a more refined version of these two local conditions we provide a deterministic algorithm that obtains a Frieze-Kannan regular partition of any graph G in time O(|V(G)|(2)).