Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
N. Kahale , Lab. for Comput. Sci., MIT, Cambridge, MA, USA
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.
expanders, Ramanujan graphs, expansion properties, regular graphs, explicit k-regular graphs, eigenvalue, random walks
N. Kahale, "Better expansion for Ramanujan graphs,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 398-404.