Cyclic Sums, Network Sharing and Restricted Edge Cuts in Graphs with Long Cycles
Dieter Rautenbach , Lutz Volkmann
Preprint series: 07-06, 8
MSC 2000
05A17 Partitions of integers
05C40 Connectivity
Abstract
We study graphs G = (V,E) containing a long cycle which for given
integers a1, a2, ..., ak 2 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.
Keywords: restricted edge connectivity, arbitrarily vertex decomposable
graph, network reliability, network sharin
