Combinatorica
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q
Journal of Combinatorial Theory Series B
Random lifts of graphs: independence and chromatic number
Random Structures & Algorithms
Random Lifts of Graphs: Edge Expansion
Combinatorics, Probability and Computing
Random Lifts Of Graphs: Perfect Matchings
Combinatorica
Word maps and spectra of random graph lifts
Random Structures & Algorithms
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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 G1 and G2, if V(H) = V(G1) × V(G2) and both projection maps V(H)→V(G1) and V(H)→V(G2) 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(d3/4). This construction resembles random graph lifts, but requires fewer random bits. © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc.