EXPANDER GRAPHS AND SIEVING IN COMBINATORIAL STRUCTURES
نویسندگان
چکیده
منابع مشابه
Expander Graphs
This paper will introduce expander graphs. Kolmogorov and Barzdin’s proof on the three dimensional realization of networks will be discussed as one of the first examples of expander graphs. The last section will discuss error correcting code as an application of expander graphs to computer science.
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Acknowledgments First of all I want to thank my advisor, Stefan Felsner. In lectures and many discussions I learned a lot from him not only about graph theory and combinatorics. He was also willing to share the large and little tricks and insights that make (scientific) working so much easier. During lunches and many coffee breaks I also learned a lot from Stefan about life, the universe, and e...
متن کاملExpander Graphs
Let AG be the adjacency matrix of G. Let λ1 ≥ λ2 ≥ . . . ≥ λn be the eigenvalues of AG. Sometimes we will also be interested in the Laplacian matrix of G. This is defined to be LG = D−AG, where D is the diagonal matrix where Dvv equals the degree of the vertex v. For d-regular graphs, LG = dI −AG, and hence the eigenvalues of LG are d− λ1, d− λ2, . . . , d− λn. Lemma 1. • λ1 = d. • λ2 = λ3 = . ...
متن کاملWalks , and Expander Graphs
I have three goals for this lecture. The first is to introduce one of the most important familes of graphs: expander graphs. They are the source of much combinatorial power, and the counterexample to numerous conjectures. We will become acquainted with these graphs by examining random walks on them. To facilitate the analysis of random walks, we will examine these graphs through their adjacency...
متن کاملLecture 17: Expander Graphs 1 Overview of Expander Graphs
Let G = (V,E) be an undirected d-regular graph, here, |V | = n, deg(u) = d for all u ∈ V . We will typically interpret the properties of expander graphs in an asymptotic sense. That is, there will be an infinite family of graphs G, with a growing number of vertices n. By “sparse”, we mean that the degree d of G should be very slowly growing as a function of n. When n goes to infinity (n → ∞), d...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2018
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788717000234