Quasirandom Cayley graphs
We prove that the properties of having small discrepancy and having small second eigenvalue are equivalent in Cayley graphs, extending a result of Kohayakawa, R¨odl, and Schacht, who treated the abelian case. The proof relies on Grothendieck’s inequality. As a corollary, we also prove that a similar...
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| Format: | Journal article |
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Discrete Analysis
2017
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| Sažetak: | We prove that the properties of having small discrepancy and having small second eigenvalue are equivalent in Cayley graphs, extending a result of Kohayakawa, R¨odl, and Schacht, who treated the abelian case. The proof relies on Grothendieck’s inequality. As a corollary, we also prove that a similar result holds in all vertex-transitive graphs. |
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