One-to-One Disjoint Path Covers on WK-Networks

Abstract

The WK-recursive network denoted by K(d, t) has received much attention due to its many favorable properties. We use O i to denote the open vertex set of K i (d, t−1) with 1 ≤ i ≤ d and let O I = {O i |1 ≤ i ≤ d}. We prove that given any node μ and a set of distinct destination nodes T = {t j |1 ≤ j ≤ d−1} where t j ∉ O I , and μ, t j are not in the same subgraph, there exist d−1 node-disjoint paths between μ and T whose union covers all the vertices of K(d, t) where d≥4 and t≥1.