Cyclic sums, network sharing, and restricted edge cuts in graphs with long cycles

Abstract

AbstractWe study graphs G = (V,E) containing a long cycle which for given integers a1, a2,…,ak ∈ \input amssym ${\Bbb N}$ have an edge cut whose removal results in k components with vertex sets V1,V2,…,Vk such that |Vi| ≥ ai for 1 ≤ i ≤ k. Our results closely relate to problems and recent research in network sharing and network reliability. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008