## 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.

Original language | American English |
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Title of host publication | Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019 |

Publisher | IEEE Computer Society |

Pages | 158-170 |

Number of pages | 13 |

ISBN (Electronic) | 9781728149523 |

DOIs | |

State | Published - Nov 2019 |

Event | 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 - Baltimore, United States Duration: 9 Nov 2019 → 12 Nov 2019 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 2019-November |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 |
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Country/Territory | United States |

City | Baltimore |

Period | 9/11/19 → 12/11/19 |

### Bibliographical note

Publisher Copyright:© 2019 IEEE.

## Keywords

- Expander-Graphs
- High-dimensional Combinatorics