@inproceedings{ab99568f3a5443569c081d336e9e9310,
title = "Expander graphs-both local and global",
abstract = "Let G=(V,E) be a finite graph. For v V we denote by G-v the subgraph of G that is induced by v's neighbor set. We say that G is (a,b)-regular for a>b>0 integers, if G is a-regular and G-v is b-regular for every v V. Recent advances in PCP theory call for the construction of infinitely many (a,b)-regular expander graphs G that are expanders also locally. Namely, all the graphs \{G-v|v V\} should be expanders as well. While random regular graphs are expanders with high probability, they almost surely fail to expand locally. Here we construct two families of (a,b)-regular graphs that expand both locally and globally. We also analyze the possible local and global spectral gaps of (a,b)-regular graphs. In addition, we examine our constructions vis-A-vis properties which are considered characteristic of high-dimensional expanders.",
keywords = "Expander-Graphs, High-dimensional Combinatorics",
author = "Michael Chapman and Nati Linial and Yuval Peled",
note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 ; Conference date: 09-11-2019 Through 12-11-2019",
year = "2019",
month = nov,
doi = "10.1109/FOCS.2019.00019",
language = "الإنجليزيّة",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "158--170",
booktitle = "Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019",
address = "الولايات المتّحدة",
}