{"paper":{"title":"Rainbow Tur\\'an Problem for Even Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Choongbum Lee, Shagnik Das","submitted_at":"2012-02-15T07:31:35Z","abstract_excerpt":"An edge-colored graph is rainbow if all its edges are colored with distinct colors. For a fixed graph $H$, the rainbow Tur\\'an number $\\mathrm{ex}^{\\ast}(n,H)$ is defined as the maximum number of edges in a properly edge-colored graph on $n$ vertices with no rainbow copy of $H$. We study the rainbow Tur\\'an number of even cycles, and prove that for every fixed $\\varepsilon > 0$, there is a constant $C(\\varepsilon)$ such that every properly edge-colored graph on $n$ vertices with at least $C(\\varepsilon) n^{1 + \\varepsilon}$ edges contains a rainbow cycle of even length at most $2 \\lceil \\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3221","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"}