## Abstract

In this article, we study a new product of graphs called tight product. A graph H is said to be a tight product of two (undirected multi) graphs G _{1} and G_{2}, if V(H) = V(G_{1}) × V(G _{2}) and both projection maps V(H)→V(G_{1}) and V(H)→V(G_{2}) are covering maps. It is not a priori clear when two given graphs have a tight product (in fact, it is NP-hard to decide). We investigate the conditions under which this is possible. This perspective yields a new characterization of class-1 (2k+ 1)-regular graphs. We also obtain a new model of random d-regular graphs whose second eigenvalue is almost surely at most O(d^{3/4}). This construction resembles random graph lifts, but requires fewer random bits.

Original language | American English |
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Pages (from-to) | 426-440 |

Number of pages | 15 |

Journal | Journal of Graph Theory |

Volume | 69 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2012 |

## Keywords

- expanders
- lifts of graphs
- random graphs