{"paper":{"title":"Rainbow Tur\\'an problems for paths and forests of stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amites Sarkar, Cory Palmer, Daniel Johnston","submitted_at":"2016-08-31T23:57:08Z","abstract_excerpt":"For a fixed graph $F$, we would like to determine the maximum number of edges in a properly edge-colored graph on $n$ vertices which does not contain a {\\emph rainbow copy} of $F$, that is, a copy of $F$ all of whose edges receive a different color. This maximum, denoted by $ex^*(n,F)$, is the {\\emph rainbow Tur\\'an number} of $F$, and its systematic study was initiated by Keevash, Mubayi, Sudakov and Verstra\\\"ete in 2007. We determine $ex^*(n,F)$ exactly when $F$ is a forest of stars, and give bounds on $ex^*(n,F)$ when $F$ is a path with $k$ edges, disproving a conjecture in Keevash et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00069","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"}