Edge-connectivity augmentation of a graph

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

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Abstract

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:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
izr. prof. dr. Arjana Žitnik		Mentor

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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