Ghandehari, Mahya (2005) Independent sets in graph products via harmonic analysis. Masters thesis, Concordia University.
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In this thesis we study the independent sets of Knr , the weak product of n complete graphs on r vertices, which are close to be of maximum size. We review the previously known results. For constant r and arbitrary n, it was known that every such independent set is close to some independent set of maximum size. We prove that this statement holds for arbitrary r and n. The proof involves some techniques from Fourier analysis of Boolean functions on Znr . In fact we show that when most of the 2-norm weight of the Fourier expansion of a Boolean function on Znr is concentrated on the first two levels, then the function can be approximated by a Boolean function that depends only on one coordinate. A stronger analogue of this has been proven by Jean Bourgain for Zn2 . We present an expanded version of his proof in this thesis.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Thesis (Masters)|
|Pagination:||v, 57 leaves ; 29 cm.|
|Degree Name:||M. Sc.|
|Program:||Mathematics and Statistics|
|Thesis Supervisor(s):||Larose, Benoit|
|Deposited By:||Concordia University Libraries|
|Deposited On:||18 Aug 2011 14:28|
|Last Modified:||18 Aug 2011 14:28|
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