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Dissertations / Theses on the topic 'Graphs theory'

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Published: 4 June 2021

Last updated: 26 July 2025

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1

Bessy, Stéphane. "Some problems in graph theory and graphs algorithmic theory." Habilitation à diriger des recherches, Université Montpellier II - Sciences et Techniques du Languedoc, 2012. http://tel.archives-ouvertes.fr/tel-00806716.

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This document is a long abstract of my research work, concerning graph theory and algorithms on graphs. It summarizes some results, gives ideas of the proof for some of them and presents the context of the different topics together with some interesting open questions connected to them The first part precises the notations used in the rest of the paper; the second part deals with some problems on cycles in digraphs; the third part is an overview of two graph coloring problems and one problem on structures in colored graphs; finally the fourth part focus on some results in algorithmic graph the

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2

Myers, Joseph Samuel. "Extremal theory of graph minors and directed graphs." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619614.

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3

Badaoui, Mohamad. "G-graphs and Expander graphs." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMC207/document.

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L’utilisation de l’algèbre pour résoudre des problèmes de graphes a conduit au développement de trois branches : théorie spectrale des graphes, géométrie et combinatoire des groupes et études des invariants de graphes. La notion de graphe d’expansions (invariant de graphes) est relativement récente, elle a été développée afin d’étudier la robustesse des réseaux de télécommunication. Il s’avère que la construction de familles infinies de graphes expanseurs est un problème difficile. Cette thèse traite principalement de la construction de nouvelles familles de tels graphes. Les graphes expanseur

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4

Khouzam, Nelly. "A new class of brittle graphs /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66048.

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5

Sen, Sagnik. "A contribution to the theory of graph homomorphisms and colorings." Phd thesis, Bordeaux, 2014. http://tel.archives-ouvertes.fr/tel-00960893.

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Dans cette thèse, nous considérons des questions relatives aux homomorphismes de quatre types distincts de graphes : les graphes orientés, les graphes orientables, les graphes 2-arête colorés et les graphes signés. Pour chacun des ces quatre types, nous cherchons à déterminer le nombre chromatique, le nombre de clique relatif et le nombre de clique absolu pour différentes familles de graphes planaires : les graphes planaires extérieurs, les graphes planaires extérieurs de maille fixée, les graphes planaires et les graphes planaires de maille fixée. Nous étudions également les étiquetages "2-di

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6

Hoang, Chinh T. "Perfect graphs." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74011.

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7

Lamb, John D. "Theory of bond graphs." Thesis, University of Nottingham, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239418.

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8

Borinsky, Michael. "Graphs in perturbation theory." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19201.

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Inhalt dieser Arbeit ist eine Erweiterung der Hopfalgebrastruktur der Feynmangraphen und Renormierung von Connes und Kreimer. Zusätzlich wird eine Struktur auf faktoriell wachsenden Potenzreihen eingeführt, die deren asymptotisches Wachstum beschreibt und die kompatibel mit der Hopfalgebrastruktur ist. Die Hopfalgebrastruktur auf Graphen erlaubt die explizite Enumeration von Graphen mit Einschränkungen in Bezug auf die erlaubten Untergraphen. Im Fall der Feynmangraphen wird zusätzlich eine algebraische Verbandstruktur eingeführt, die weitere eindeutige Eigenschaften von physikalischen Quan

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9

Olariu, Stephan. "Results on perfect graphs." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=73997.

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10

Yang, Weihua. "Supereulerian graphs, Hamiltonicity of graphes and several extremal problems in graphs." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00877793.

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In this thesis, we focus on the following topics: supereulerian graphs, hamiltonian line graphs, fault-tolerant Hamiltonian laceability of Cayley graphs generated by transposition trees, and several extremal problems on the (minimum and/or maximum) size of graphs under a given graph property. The thesis includes six chapters. The first one is to introduce definitions and summary the main results of the thesis, and in the last chapter we introduce the furture research of the thesis. The main studies in Chapters 2 - 5 are as follows. In Chapter 2, we explore conditions for a graph to be supereul

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11

Hayward, Ryan B. "Two classes of perfect graphs." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74025.

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12

Duffy, Christopher. "Homomorphisms of (j, k)-mixed graphs." Thesis, Bordeaux, 2015. http://hdl.handle.net/1828/6601.

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A mixed graph is a simple graph in which a subset of the edges have been assigned directions to form arcs. For non-negative integers j and k, a (j, k)−mixed graph is a mixed graph with j types of arcs and k types of edges. The collection of (j, k)−mixed graphs contains simple graphs ((0,1)−mixed graphs), oriented graphs ((1,0)-mixed graphs) and k−edge-coloured graphs ((0, k)−mixed graphs). A homomorphism is a vertex mapping from one (j,k)−mixed graph to another in which edge type is preserved, and arc type and direction are preserved. An m−colouring of a (j, k)−mixed graph is a homomorphism f

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13

Mighton, John 1957. "Knot theory on bipartite graphs." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ49930.pdf.

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14

Backman, Spencer Christopher Foster. "Combinatorial divisor theory for graphs." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51908.

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Chip-firing is a deceptively simple game played on the vertices of a graph, which was independently discovered in probability theory, poset theory, graph theory, and statistical physics. In recent years, chip-firing has been employed in the development of a theory of divisors on graphs analogous to the classical theory for Riemann surfaces. In particular, Baker and Norin were able to use this set up to prove a combinatorial Riemann-Roch formula, whose classical counterpart is one of the cornerstones of modern algebraic geometry. It is now understood that the relationship between divisor theor

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15

Zuffi, Lorenzo. "Simplicial Complexes From Graphs Toward Graph Persistence." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13519/.

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Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph

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16

Möller, Rögnvaldur G. "Groups acting on graphs." Thesis, University of Oxford, 1991. http://ora.ox.ac.uk/objects/uuid:2dacfc67-56c4-4541-b52e-10199a13dcc2.

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In the first part of this thesis we investigate the automorphism groups of regular trees. In the second part we look at the action of the automorphism group of a locally finite graph on the ends of the graph. The two part are not directly related but trees play a fundamental role in both parts. Let T<sub>n</sub> be the regular tree of valency n. Put G := Aut(T<sub>n</sub>) and let G<sub>0</sub> be the subgroup of G that is generated by the stabilisers of points. The main results of the first part are : Theorem 4.1 Suppose 3 ≤ n < N<sub>0</sub> and α ϵ T<sub>n</sub>. Then G<sub>α</sub> (the sta

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17

Jagger, Christopher Neil. "Partitions of graphs." Thesis, University of Cambridge, 1995. https://www.repository.cam.ac.uk/handle/1810/251583.

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18

Al-Doujan, Fawwaz Awwad. "Spectra of graphs." Thesis, University of East Anglia, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306195.

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19

Lim, Daekeun. "Cycles and Cliques in Steinhaus Graphs." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc278469/.

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In this dissertation several results in Steinhaus graphs are investigated. First under some further conditions imposed on the induced cycles in steinhaus graphs, the order of induced cycles in Steinhaus graphs is at most [(n+3)/2]. Next the results of maximum clique size in Steinhaus graphs are used to enumerate the Steinhaus graphs having maximal cliques. Finally the concept of jumbled graphs and Posa's Lemma are used to show that almost all Steinhaus graphs are Hamiltonian.

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20

Meek, Darrin Leigh. "On graph approximation heuristics : an application to vertex cover on planar graphs." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/24088.

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21

Chan, Wai Hong. "Bandwidth problems of graphs." HKBU Institutional Repository, 1996. http://repository.hkbu.edu.hk/etd_ra/62.

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22

Thwaites, Peter. "Chain event graphs : theory and application." Thesis, University of Warwick, 2008. http://wrap.warwick.ac.uk/49194/.

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This thesis is concerned with the Graphical model known as the Chain Event Graph (CEG) [1][60][61], and develops the theory that appears in the currently published papers on this work. Results derived are analogous to those produced for Bayesian Networks (BNs), and I show that for asymmetric problems the CEG is generally superior to the BN both as a representation of the problem and as an analytical tool. The CEG is designed to embody the conditional independence structure of problems whose state spaces are asymmetric and do not admit a natural Product Space structure. In this they differ from

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23

Wagner, Peter. "The Ramsey theory of multicoloured graphs." Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614225.

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24

Macon, Lisa Fischer. "Almost regular graphs and edge-face colorings of plane graphs." Orlando, Fla. : University of Central Florida, 2009. http://purl.fcla.edu/fcla/etd/CFE0002507.

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25

Ross, Christopher Jon. "Properties of Random Threshold and Bipartite Graphs." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306296991.

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26

Pearce, Geoffrey. "Transitive decompositions of graphs." University of Western Australia. School of Mathematics and Statistics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0087.

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A transitive decomposition of a graph is a partition of the arc set such that there exists a group of automorphisms of the graph which preserves and acts transitively on the partition. This turns out to be a very broad idea, with several striking connections with other areas of mathematics. In this thesis we first develop some general theory of transitive decompositions, and in particular we illustrate some of the more interesting connections with certain combinatorial and geometric structures. We then give complete, or nearly complete, structural characterisations of certain classes of transi

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27

Wojciechowska, Iwona. "Broadcasting in grid graphs." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=877.

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Thesis (Ph. D.)--West Virginia University, 1999.<br>Title from document title page. Document formatted into pages; contains vii, 69 p. : ill. Includes abstract. Includes bibliographical references (p. 67-69).

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28

Montgomery, Bruce Lee. "Dynamic coloring of graphs." Morgantown, W. Va. : [West Virginia University Libraries], 2001. http://etd.wvu.edu/templates/showETD.cfm?recnum=2109.

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Thesis (Ph. D.)--West Virginia University, 2001.<br>Title from document title page. Document formatted into pages; contains viii, 52 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 51).

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29

Yerger, Carl Roger Jr. "Color-critical graphs on surfaces." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37197.

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A graph is (t+1)-critical if it is not t-colorable, but every proper subgraph is. In this thesis, we study the structure of critical graphs on higher surfaces. One major result in this area is Carsten Thomassen's proof that there are finitely many 6-critical graphs on a fixed surface. This proof involves a structural theorem about a precolored cycle C of length q. In general terms, he proves that a coloring, c, of C, can be extended inside the cycle, or there exists a subgraph H with at most a number of vertices exponential in q such that c can not be extended to a 5-coloring of H. In Cha

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30

Jonsson, Jakob. "Simplicial complexes of graphs /." Berlin [u.a.] : Springer, 2008. http://dx.doi.org/10.1007/978-3-540-75858-7.

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31

Meagher, Karen. "Covering arrays on graphs: Qualitative independence graphs and extremal set partition theory." Thesis, University of Ottawa (Canada), 2005. http://hdl.handle.net/10393/29234.

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There has been a good deal of research on covering arrays over the last 20 years. Most of this work has focused on constructions, applications and generalizations of covering arrays. The main focus of this thesis is a generalization of covering arrays, covering arrays on graphs. The original motivation for this generalization was to improve applications of covering arrays to testing systems and networks, but this extension also gives us new ways to study covering arrays. Two vectors v, w in Znk are qualitatively independent if for all ordered pairs (a, b) ∈ Zk x Zk there is a po

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32

Reed, Bruce. "A semi-strong perfect graph theorem /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72812.

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33

Dey, Sanjoy. "Structural properties of visibility and weak visibility graphs." Virtual Press, 1997. http://liblink.bsu.edu/uhtbin/catkey/1048394.

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Given a finite set S of n nonintersecting line segments with no three end points collinear, the segment end point visibility graph is defined as the graph whose vertices are the end points of the line segments in S and two vertices are adjacent if the straight line segment joining two end points does not intersect any element of S, or if they are end points of the same segment. Segment end point visibility graphs have a wide variety of applications in VLSI circuit design, study of art gallery problems, and other areas of computational geometry. This thesis contains a survey of the important re

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34

Williams, Trevor K. "Combinatorial Games on Graphs." DigitalCommons@USU, 2017. https://digitalcommons.usu.edu/etd/6502.

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Combinatorial games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games along with some educational tools were developed in the pursuit of the solution of these games. The game of Nim is at least centuries old, possibly originating in China, but noted in the 16th century in European countries. It consists of several stacks of tokens, and two players alternate taking one or more tokens from one of the stacks, and the player who cannot make a move loses. The fo

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35

Wang, Jiaxin. "Various pushing methods on grid graphs." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=839.

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Thesis (M.S.)--West Virginia University, 1999.<br>Title from document title page. Document formatted into pages; contains v, 39 p. : ill. (some col.) Includes abstract. Includes bibliographical references (p. 39).

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36

Hunt, D'Hania J. "Constructing higher-order de Bruijn graphs." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2002. http://library.nps.navy.mil/uhtbin/hyperion-image/02Jun%5FHunt.pdf.

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Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, June 2002.<br>Thesis advisor(s): Harold Fredricksen, Craig W. Rasmussen. Includes bibliographical references (p. 45-46). Also available online.

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37

Weinstein, Lee. "Empirical study of graph properties with particular interest towards random graphs." Diss., Connect to the thesis, 2005. http://hdl.handle.net/10066/1485.

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38

Bowlin, Garry. "Maximum frustration of bipartite signed graphs." Diss., Online access via UMI:, 2009.

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39

Song, Zengmin. "Cycles and coloring in graphs." HKBU Institutional Repository, 2001. http://repository.hkbu.edu.hk/etd_ra/285.

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40

Hill, Alan. "Self-Dual Graphs." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1014.

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The study of self-duality has attracted some attention over the past decade. A good deal of research in that time has been done on constructing and classifying all self-dual graphs and in particular polyhedra. We will give an overview of the recent research in the first two chapters. In the third chapter, we will show the necessary condition that a self-complementary self-dual graph have <i>n</i> ≡ 0, 1 (mod 8) vertices and we will review White's infinite class (the Paley graphs, for which <i>n</i> ≡ 1 (mod 8)). Finally, we will construct a new infinite class of self-co

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41

Okitowamba, Onyumbe. "Groupoids of homogeneous factorisations of graphs." Thesis, University of the Western Cape, 2009. http://hdl.handle.net/11394/2690.

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Magister Scientiae - MSc<br>This thesis is a study on the confluence of algebraic structures and graph theory. Its aim is to consider groupoids from factorisations of complete graphs. We are especially interested in the cases where the factors are isomorphic. We analyse the loops obtained from homogeneous factorisations and ask if homogeneity is reflected in the kind of loops that are obtained. In particular, we are interested to see if we obtain either groups or quasi-associative Cayley sets from these loops. November 2008.<br>South Africa

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42

Ali, Seema. "Colouring generalized Kneser graphs and homotopy theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0014/MQ34938.pdf.

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43

Dickson, James Odziemiec. "An Introduction to Ramsey Theory on Graphs." Thesis, Virginia Tech, 2011. http://hdl.handle.net/10919/32873.

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44

Brody, Justin. "On the model theory of random graphs." College Park, Md. : University of Maryland, 2009. http://hdl.handle.net/1903/9291.

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Thesis (Ph.D.) -- University of Maryland, College Park, 2009.<br>Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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45

Hearn, John. "Kolmogorov Complexity of Graphs." Scholarship @ Claremont, 2006. https://scholarship.claremont.edu/hmc_theses/182.

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Kolmogorov complexity is a theory based on the premise that the complexity of a binary string can be measured by its compressibility; that is, a string’s complexity is the length of the shortest program that produces that string. We explore applications of this measure to graph theory.

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46

Jahanbakht, Nafiseh, and University of Lethbridge Faculty of Arts and Science. "Energy of graphs and digraphs." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2010, 2010. http://hdl.handle.net/10133/2489.

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The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. The concept is related to the energy of a class of molecules in chemistry and was first brought to mathematics by Gutman in 1978 ([8]). In this thesis, we do a comprehensive study on the energy of graphs and digraphs. In Chapter 3, we review some existing upper and lower bounds for the energy of a graph. We come up with some new results in this chapter. A graph with n vertices is hyper-energetic if its energy is greater than 2n−2. Some classes of graphs are proved to be hyper-energetic. We find

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47

Enciso, Rosa. "Alliances in Graphs: Parameterized Algorithms and on Partitioning Series-Parallel Graphs." Doctoral diss., University of Central Florida, 2009. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2479.

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Alliances are used to denote agreements between members of a group with similar interests. Alliances can occur between nations, biological sequences, business cartels, and other entities. The notion of alliances in graphs was first introduced by Kristiansen, Hedetniemi, and Hedetniemi in . A defensive alliance in a graph G=(V,E) is a non empty set S⊆V S where, for all x ∈S, |N∩S|≥|N-S|. Consequently, every vertex that is a member of a defensive alliance has at least as many vertices defending it as there are vertices attacking it. Alliances can be used to model a variet

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48

Ferra, Gomes de Almeida Girão António José. "Extremal and structural problems of graphs." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/285427.

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In this dissertation, we are interested in studying several parameters of graphs and understanding their extreme values. We begin in Chapter~$2$ with a question on edge colouring. When can a partial proper edge colouring of a graph of maximum degree $\Delta$ be extended to a proper colouring of the entire graph using an `optimal' set of colours? Albertson and Moore conjectured this is always possible provided no two precoloured edges are within distance $2$. The main result of Chapter~$2$ comes close to proving this conjecture. Moreover, in Chapter~$3$, we completely answer the previous questi

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Heckman, Christopher Carl. "Independent sets in bounded degree graphs." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/29163.

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Lo, Allan. "Cliques in graphs." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/237438.

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The main focus of this thesis is to evaluate .k_r(n,\delta)., the minimal number of $r$-cliques in graphs with $n$ vertices and minimum degree~$\delta$. A fundamental result in Graph Theory states that a triangle-free graph of order $n$ has at most $n 2/4$ edges. Hence, a triangle-free graph has minimum degree at most $n/2$, so if $k_3(n,\delta) =0$ then $\delta \le n/2$. For $n/2 \leq \delta \leq 4n/5$, I have evaluated $k_r(n,\delta)$ and determined the structures of the extremal graphs. For $\delta \ge 4n/5$, I give a conjecture on $k_r(n,\delta)$, as well as the structures of these extrema

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