{"paper":{"title":"Anti-Ramsey numbers of graphs with small connected components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shoni Gilboa, Yehuda Roditty","submitted_at":"2013-10-16T11:10:46Z","abstract_excerpt":"The anti-Ramsey number, $AR(n,G)$, for a graph $G$ and an integer $n\\geq|V(G)|$, is defined to be the minimal integer $r$ such that in any edge-colouring of $K_n$ by at least $r$ colours there is a multicoloured copy of $G$, namely, a copy of $G$ that each of its edges has a distinct colour. In this paper we determine, for large enough $n$, $AR(n,L\\cup tP_2)$ and $AR(n,L\\cup kP_3)$ for any large enough $t$ and $k$, and a graph $L$ satisfying some conditions. Consequently, we determine $AR(n,G)$, for large enough $n$, where $G$ is $P_3\\cup tP_2$ for any $t\\geq 3$, $P_4\\cup tP_2$ and $C_3\\cup tP"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4331","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"}