{"paper":{"title":"On sufficient conditions for rainbow cycles in edge-colored graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Chuandong Xu, Shenggui Zhang, Shinya Fujita","submitted_at":"2017-05-10T09:43:53Z","abstract_excerpt":"Let $G$ be an edge-colored graph. We use $e(G)$ and $c(G)$ to denote the number of edges of $G$ and the number of colors appearing on $E(G)$, respectively. For a vertex $v\\in V(G)$, the \\emph{color neighborhood} of $v$ is defined as the set of colors assigned to the edges incident to $v$. A subgraph of $G$ is \\emph{rainbow} if all of its edges are assigned with distinct colors. The well-known Mantel's theorem states that a graph $G$ on $n$ vertices contains a triangle if $e(G)\\geq\\lfloor\\frac{n^2}{4}\\rfloor+1$. Rademacher (1941) showed that $G$ contains at least $\\lfloor\\frac{n}{2}\\rfloor$ tri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03675","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"}