拉马努金图的更好展开

[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science Pub Date : 1991-09-01 DOI:10.1109/SFCS.1991.185397

N. Kahalé

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引用次数: 25

摘要

研究正则图的展开性质。关于显式k正则图的线性大小的子集的最好的已知展开是k/4。该界是由k=p+1阶的非二部Ramanujan图实现的，该图具有除最大特征值以外的所有特征值的绝对值不超过2根号p的性质。将非二部Ramanujan图的线性子集的展开系数提高到3(k-2)/8。建立了其他结果，包括扩展器上随机漫步的改进结果。

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Better expansion for Ramanujan graphs

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.<>

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[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science

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