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Edge-connectivity augmentation of a graph

Jan Geršak (2018) Edge-connectivity augmentation of a graph. EngD thesis.

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    In this thesis we consider the edge-connectivity augmentation problem. In the first part of the thesis we present a cactus representation of a graph and describe its construction for which we present an algorithm. In the second part of the thesis we consider the relation between edge-connectivity of a graph and its cactus representation. Using this relation we give a lower bound for the least number of edges to be added to increase the edge-connectivity of a graph by one. We also prove that the lower bound is always achievable. Then we give an algorithm for edge-connectivity augmentation by one by applying properties of the cycle-type normal cactus representation. In the third part of the thesis we present general edge splitting method which is used in Frank's algorithm for solving edge-connectivity augmentation problem. We also prove Mader's theorem which is needed to prove finiteness of edge splitting in Frank's algorithm.

    Item Type: Thesis (EngD thesis)
    Keywords: graph, cactus representation, edge connectivity augmentation, edge splitting, Frank's algorithm, Mader's theorem.
    Number of Pages: 53
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    izr. prof. dr. Arjana ŽitnikMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1537969091)
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 4245
    Date Deposited: 19 Sep 2018 18:39
    Last Modified: 11 Oct 2018 10:11
    URI: http://eprints.fri.uni-lj.si/id/eprint/4245

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