Independent sets in graph products via harmonic analysis
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 m...
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| Format: | Others |
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2005
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| Online Access: | http://spectrum.library.concordia.ca/8540/1/MR10211.pdf Ghandehari, Mahya <http://spectrum.library.concordia.ca/view/creators/Ghandehari=3AMahya=3A=3A.html> (2005) Independent sets in graph products via harmonic analysis. Masters thesis, Concordia University. |
| Summary: | 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. |
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