{"paper":{"title":"Tight products and Expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Amit Daniely, Nathan Linial","submitted_at":"2010-01-20T20:14:15Z","abstract_excerpt":"In this paper we study a new product of graphs called {\\em 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 eig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3661","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}