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 41 for “"Erdos"”.
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Erdos-Posa theorems for undirected group-labelled graphs
Erdős and Pósa proved in 1965 that cycles satisfy an approximate packing-covering duality. Finding analogous approximate dualities for other families of graphs has since become a highly active area of research due in part to its algorithmic applications. In this thesis we investigate the Erdős-Pósa …
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Tournaments With Forbidden Substructures and the Erdos-Hajnal Conjecture
A celebrated Conjecture of Erdos and Hajnal states that for every undirected graph H there exists ɛ(H)>0 such that every undirected graph on n vertices that does not contain H as an induced subgraph contains a clique or a stable set of size at least n^{ɛ(H)}. In 2001 Alon, Pach and Solymosi proved …
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Extremal graph theory: supersaturation and enumeration
… 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 classical result of Kolaitis, Promel and Rothschild on the typical structure of …
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Local Algorithms for Sparsification of Average-case Graphs
… by considering average-case graphs such as Erdos-Renyi random graphs and the Preferential Attachment model. We first present an LCA algorithm which, on an Erdos-Renyi graph input 𝐺 with edge parameter 𝑝 ≥ Ω(log(𝑛) 𝑛 ), gives fast access to a sparsification 𝐺′ of 𝐺, such that 𝐺′ is connected …
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Enumeration Results On Leaf Labeled Trees
… of categories of phylogenetic trees. P.L. Erdos and L.A. Szekely [Adv. Appl. Math.series 10,1989, 488--496] gave a bijection between rooted semilabeled trees and set partitions. L.H. Harper's results [Ann. Math.Stat.series 38, 1967, 410--414] on the asymptotic normality of the Stirling …
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The sum-product problem
The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many products or many sums. We explore quantitative aspects of the problem over both the real numbers and finite fields of prime order.
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Extremal problems for cycles in graphs and hypergraphs
… or long paths, extending famous results of Erdos and Gallai. Results include bounds on the size of such objects as well as stability theorems about the structure of extremal and almost extremal objects.
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Extremal Problems in Graph Theory: Degree Sequences, Distance, Colorings, and Labelings
… best (probabilistic) bound of On (due to Erdos and Gyarfas).
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Extremal problems in pseudo-random graphs and asymptotic enumeration
… We study one such question -- a conjecture of Erdos, Faudree, and Sos regarding the orders and sizes of induced subgraphs of Ramsey graphs. Although we do not fully resolve this conjecture, the main theorem in the first part of this dissertation, joint work with Noga Alon, Jozsef Balogh, and …
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Degree sequences
… These characterizations imply theorems due to P. Erdos, M. S. Jacobson and J. Lehel, R. J. Gould, M. S. Jacobson and J. Lehel and C. H. Lai.
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(Visible) Tilings of Squares and Hypercubes
More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit square.Here we consider various classes of tilings , this is, packings where there is no empty space inside the unit square. Several types of questions will be explored here. Various construction …
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Covering Systems
… or covering system. A famous conjecture of Erdos from 1950 states that the least modulus of a covering system can be arbitrarily large. This conjecture remains open, and, in its full strength, appears at present to be unattackable. Most of the effort in this direction has been aimed at …
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Probabilistic Methods
… by Erdös Pai, better known to Westerners as Paul Erdos in the 1950s. The probabilistic method is a powerful tool for solving many problems in discrete mathematics, combinatorics and also in graph .theory. It is also very useful to solve problems in number theory, combinatorial geometry, linear …
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Covering Systems of Polynomial Rings Over Finite Fields
In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with distinct moduli. He called such systems of congruences covering systems. Utilizing his covering system, he disproved a conjecture of de Polignac asking, “for every odd k, is there a prime of the form 2n …
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Improving the output of algorithms for large-scale approximate graph matching
… a partially correct correspondence between two Erdos-Renyi graphs as input, we show that our algorithm can correct all errors with high probability. Furthermore, when applied to real-world social networks, we empirically demonstrate that our algorithm can perform graph matching accurately, even …
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Cliques in block graphs of designs and orthogonal arrays
The Erdos-Ko-Rado [EKR] Theorem for intersecting families is a fundamental result in combinatorics, particularly in extremal set theory. This theorem not only establishes an upper bound on the size of the largest intersecting family but also characterizes the families that attain this bound—–these …
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Extremal graph theory: Ramsey-Turán numbers, chromatic thresholds, and minors
… and hypergraphs, proving two conjectures of Erdos, Hajnal, Simonovits, Sos, and Szemeredi. In joint work with Jozsef Balogh, our first main theorem is to provide the first lower bounds of order \Omega(n^2) on RT_t(n,K_{t+2},o(n)). Our second main theorem is to prove lower bounds on …
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In-core, hint-based, speculative multithreading
State-of-the-art high-performance processors rely on instruction-level parallelism (ILP) during sequential regions. This results in excellent performance in regions that exhibit large amounts of ILP. However, gains are limited elsewhere, due to strict upper bounds, superlinear scaling of costs, and …
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Robustness of complex networks to global perturbations
… by Watts-Strogatz small-world networks and Erdos-Renyi random graphs, and then Barabasi-Albert scalefree networks are least robust among the four topologies tested. Fully connected networks used in May’s original work are found to be consistently unstable in the presence of global …
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Forbidden substructures: induced subgraphs, Ramsey games, and sparse hypergraphs
… a strong partial result toward proving the Erdos-Hajnal conjecture. In Chapter 3, we study a Ramsey-type game in an online and random setting. The player must color edges of K_n in an order chosen uniformly at random, and loses when she has created a monochromatic triangle. We provide upper …
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