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Extremal Problems for Graphs and Hypergraphs

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posted on 01.08.2021, 00:00 by Sayan Mukherjee
Given a fixed graph G and a positive integer n, the extremal number [Turan, 1941] denotes the maximum number of edges a graph on n vertices can have without copies of G. Determining the extremal number for arbitrary graphs, or even its asymptotic behavior, is a tremendously difficult problem. The work of several researchers on this problem led to the birth of the field of extremal combinatorics. In this work, we study three different extensions of the extremal number: (a) A general study of the Erdos-Komlos function, (b) The generalized Turan problem of counting triangles, and (c) The extremal number of 3-graphs.

History

Advisor

Mubayi, Dhruv

Chair

Mubayi, Dhruv

Department

Mathematics, Statistics and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Degree name

PhD, Doctor of Philosophy

Committee Member

Perkins, William Turan, Gyorgy Reyzin, Lev Sun, Xiaorui

Submitted date

August 2021

Thesis type

application/pdf

Language

en

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