Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 32 for “"extremal graph theory"”.
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Problems in Extremal Graph Theory
What is the maximum number of edges in a multigraph on n vertices if every k-set spans at most r edges? We asymptotically determine this maximum for almost all k and r as n tends to infinity, thus giving a generalization of Turan's theorem. We find exact answers in many cases, even when edges of …
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Topics in extremal graph theory
New results are proved on several problems in extremal graph theory.
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Problems in extremal graph theory
We consider a variety of problems in extremal graph and set theory. The {\em chromatic number} of $G$, $\chi(G)$, is the smallest integer $k$ such that $G$ is $k$-colorable. The {\it square} of $G$, written $G^2$, is the supergraph of $G$ in which also vertices within distance 2 of each other in …
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Extremal Graph Theory and Enumerative Combinatorics
<p>This thesis consists of research on two topics.The first topic is about different middle parts of trees, such as center, centroid, subtree core. In this work, we considered how far apart (with given order of the tree) two different `middle points' can be and when such maximum distances are …
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Extremal graph theory: supersaturation and enumeration
… supersaturation and enumeration problems in extremal combinatorics. In Chapter 2, with Balogh, we disprove a conjecture of Erdos and Tuza concerning the number of different ways one can create a copy of K_4, a complete graph on 4 vertices, in a K_4-free graph. In Chapter 3, we extend a …
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Three Existence Problems in Extremal Graph Theory
… three different structural questions rooted in extremal graph theory. When studying graph representations, we seek efficient ways to encode the structure of a graph. For example, an {\it interval representation} of a graph $G$ is an assignment of intervals on the real line to the vertices of $G$ …
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Results in Ramsey theory and extremal graph theory
… lower bounds on a certain quantity relating to graphs. The first problem is in Ramsey theory, while the others are in extremal graph theory. In Chapter 2, which is joint work with Vojtěch Dvořák, we consider the Ramsey number $R(F_n)$ of the fan graph $F_n$, a graph consisting of $n$ triangles …
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Topics in Stochastic Combinatorial Optimization and Extremal Graph Theory
We consider a random geometric graph, G(n, r ), constructed by placing points randomly in a square S n of area n according to a Poisson process of intensity 1, and adding an edge joining any pair of points at most distance r=r(n) apart according to the ℓinfinity -metric. We show that w.h.p. …
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Embedding problems and Ramsey-Turán variations in extremal graph theory
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-08-01
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Extremal graph theory: Ramsey-Turán numbers, chromatic thresholds, and minors
… dissertation investigates several questions in extremal graph theory and the theory of graph minors. It consists of three independent parts; the first two parts focus on questions motivated by Turan's Theorem and the third part investigates a problem related to Hadwiger's Conjecture. Let H be a …
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Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory
… we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.
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Results in Extremal Graph Theory, Ramsey Theory and Additive Combinatorics
… In Chapter 2, we consider a central problem in Extremal Graph Theory. The extremal number (or Turán number) ex(n,H) of a graph H is the maximum number of edges in an H-free graph on n vertices. It is a major area of research to better understand the extremal number of bipartite graphs. In this …
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Extremal graph theory: flag algebras, Ramsey-Turan numbers, chromatic thresholds, and sparse hypergraphs
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-07-16T19:15:45Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Hu_Ping.pdf: 911457 bytes, checksum: d58f34d1ea93d149457db170269d9561 (MD5)
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Probabilistic Methods
… discrete mathematics, combinatorics and also in graph .theory. It is also very useful to solve problems in number theory, combinatorial geometry, linear algebra and real analysis. More recently, it has been applied in the development of efficient algorithms and in the study of various …
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Extremal problems on edge-colorings, independent sets, and cycle spectra of graphs
We study problems in extremal graph theory with respect to edge-colorings, independent sets, and cycle spectra. In Chapters 2 and 3, we present results in Ramsey theory, where we seek Ramsey host graphs with small maximum degree. In Chapter 4, we study a Ramsey-type problem on edge-labeled trees, …
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Random and exact structures in combinatorics
… played a key role in additive combinatorics and extremal graph theory. More generally, however, such notions come into play in the study of combinatorial probability and the use of random processes in extremal combinatorics. In a broader view, randomness (and the pseudorandomness notions which …
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Tilings and other combinatorial results
… and three problems in combinatorial geometry, extremal graph theory and sparse Ramsey theory. We first consider tilings of $\mathbb{Z}^n$. In this setting a tile $T$ is just a finite subset of $\mathbb{Z}^n$. We say that $T$ tiles $\mathbb{Z}^n$ if the latter set admits a partition into …
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The regularity method in directed graphs and hypergraphs
… been used to tackle many embedding problems in extremal graph theory. This thesis demonstrates and develops three different techniques which can be used in conjunction with the regularity method to solve such problems. These methods enable us to prove an approximate version of the well-known …
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Geometric Graph Theory and Wireless Sensor Networks
… topology of the sensors is their visibility graph. Using a standard distributed algorithm, the sensors can build common knowledge of their network topology.</p> <p>We first study the following inverse visibility problem: What positions of sensors and obstacles define the computed visibility …
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The Chromatic Structure of Dense Graphs
This thesis focusses on extremal graph theory, the study of how local constraints on a graph affect its macroscopic structure. We primarily consider the chromatic structure: whether a graph has or is close to having some (low) chromatic number. Chapter 2 is the slight exception. We consider an …
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