{"paper":{"title":"Ramsey numbers for multiple copies of sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aurelio Sulser, Milo\\v{s} Truji\\'c","submitted_at":"2022-12-05T17:55:38Z","abstract_excerpt":"For a graph $H$ and an integer $n$, we let $nH$ denote the disjoint union of\n  $n$ copies of $H$. In 1975, Burr, Erd\\H{o}s, and Spencer initiated the study\n  of Ramsey numbers for $nH$, one of few instances for which Ramsey numbers are\n  now known precisely. They showed that there is a constant $c = c(H)$ such that\n  $r(nH) = (2|H| - \\alpha(H))n + c$, provided $n$ is sufficiently large.\n  Subsequently, Burr gave an implicit way of computing $c$ and noted that this\n  long term behaviour occurs when $n$ is triply exponential in $|H|$. Very\n  recently, Buci\\'{c} and Sudakov revived the problem an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.02455","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.02455/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}