{"paper":{"title":"Graph Products Revisited: Tight Approximation Hardness of Induced Matching, Poset Dimension and More","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Bundit Laekhanukit, Danupon Nanongkai, Parinya Chalermsook","submitted_at":"2012-12-17T20:38:28Z","abstract_excerpt":"Graph product is a fundamental tool with rich applications in both graph theory and theoretical computer science. It is usually studied in the form $f(G*H)$ where $G$ and $H$ are graphs, * is a graph product and $f$ is a graph property. For example, if $f$ is the independence number and * is the disjunctive product, then the product is known to be multiplicative: $f(G*H)=f(G)f(H)$.\n  In this paper, we study graph products in the following non-standard form: $f((G\\oplus H)*J)$ where $G$, $H$ and $J$ are graphs, $\\oplus$ and * are two different graph products and $f$ is a graph property. We show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4129","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"}