{"paper":{"title":"Circulant graphs and GCD and LCM of Subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CC","authors_text":"Igor E. Shparlinski, Joachim von zur Gathen","submitted_at":"2014-02-21T23:34:31Z","abstract_excerpt":"Given two sets $A$ and $B$ of integers, we consider the problem of finding a set $S \\subseteq A$ of the smallest possible cardinality such the greatest common divisor of the elements of $S \\cup B$ equals that of those of $A \\cup B$. The particular cases of $B = \\emptyset$ and $\\#B = 1$ are of special interest and have some links with graph theory. We also consider the corresponding question for the least common multiple of the elements. We establish NP-completeness and approximation results for these problems by relating them to the Minimum Cover Problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5449","kind":"arxiv","version":1},"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"}