2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 398-404

N. Kahale , Lab. for Comput. Sci., MIT, Cambridge, MA, USA

ABSTRACT

The expansion properties of regular graphs are investigated. The best previously known expansion of subsets of linear size of explicit k-regular graphs is k/4. This bound is achieved by nonbipartite Ramanujan graphs of degree k=p+1, which have the property that all but the largest eigenvalue have absolute value at most 2 square root p. The expansion coefficient for linear subsets for nonbipartite Ramanujan graphs is improved to 3(k-2)/8. Other results are established, including improved results about random walks on expanders.

INDEX TERMS

expanders, Ramanujan graphs, expansion properties, regular graphs, explicit k-regular graphs, eigenvalue, random walks

CITATION

N. Kahale,
"Better expansion for Ramanujan graphs",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 398-404, 1991, doi:10.1109/SFCS.1991.185397