@article {IOPORT.06045749,
    author       = {Daniely, Amit and Linial, Nathan},
    title        = {Tight products and graph expansion.},
    year         = {2012},
    journal      = {Journal of Graph Theory},
    volume       = {69},
    number       = {3-4},
    issn         = {0364-9024},
    pages        = {426-440},
    publisher    = {John Wiley \& Sons, New York, NY},
    doi          = {10.1002/jgt.20593},
    abstract     = {Summary: 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 $V(H) = V(G_{1}) \times V(G_{2})$ and both projection maps $V(H)\to V(G_{1})$ and $V(H)\to V(G_{2})$ 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.},
    identifier   = {06045749},
}