Thumbnail
Access Restriction
Subscribed

Author Kahale, Nabil
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1995
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Ramanujan graphs ♦ Eigenvalues ♦ Expander graphs ♦ Induced subgraphs ♦ Load balancing ♦ Random walks ♦ Selection networks
Abstract The spectral method is the best currently known technique to prove lower bounds on expansion. Ramanujan graphs, which have asymptotically optimal second eigenvalue, are the best-known explicit expanders. The spectral method yielded a lower bound of $\textit{k}/4$ on the expansion of linear-sized subsets of $\textit{k}-regular$ Ramanujan graphs. We improve the lower bound on the expansion of Ramanujan graphs to approximately $\textit{k}/2.$ Moreover, we construct a family of $\textit{k}-regular$ graphs with asymptotically optimal second eigenvalue and linear expansion equal to $\textit{k}/2.$ This shows that $\textit{k}/2$ is the best bound one can obtain using the second eigenvalue method. We also show an upper bound of roughly 1+k-1 . As a byproduct, we obtain improved results on random walks on expanders and construct selection networks (respectively, extrovert graphs) of smaller size (respectively, degree) than was previously known.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1995-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 42
Issue Number 5
Page Count 16
Starting Page 1091
Ending Page 1106


Open content in new tab

   Open content in new tab
Source: ACM Digital Library