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

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 sharing


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