Discrepancy and Eigenvalues of Cayley Graphs
Combinatorics
2016-10-21 v2
Abstract
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, 217-244] for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.
Keywords
Cite
@article{arxiv.1602.02291,
title = {Discrepancy and Eigenvalues of Cayley Graphs},
author = {Yoshiharu Kohayakawa and Vojtěch Rödl and Mathias Schacht},
journal= {arXiv preprint arXiv:1602.02291},
year = {2016}
}
Comments
Dedicated to the memory of Professor Miroslav Fiedler, 33 pages, second version addresses changes arising from the referee report and includes an appendix with an earlier argument