Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, January 13, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Mathias Schacht (HU Berlin)

Discrepancy and Eigenvalues of Cayley Graphs

We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This positively answers a question of Chung and Graham ["Sparse quasi-random graphs'', Combinatorica 22 (2002), no. 2, pp. 217-244] for the particular case of abelian Cayley graphs, while in general the answer is negative.

(This is joint work with Yoshiharu Kohayakawa (Universidade de São Paulo) and Vojtěch Rödl (Emory University).)

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