{"paper":{"title":"Anti-Ramsey number of intersecting cliques","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Xinxin Ma, Xinyue Luo","submitted_at":"2025-07-17T14:31:49Z","abstract_excerpt":"An edge-colored graph is called a rainbow graph if all its edges have distinct colors. The anti-Ramsey number $ar(n, G)$, for a graph $G$ and a positive integer $n$, is defined as the minimum number of colors $r$ such that every exact $r$-edge-coloring of the complete graph $K_n$ contains at least one rainbow copy of $G$. A $(k, r)$-fan graph, denoted $F_{k, r}$, is a graph composed of $k$ cliques each of size $r$, all intersecting at exactly one common vertex. In this paper, we determine $ar(n, F_{k, r})$ for $n \\geq 256r^{16}(k+1)^5$, $k \\geq 1$, and $r \\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13165","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/2507.13165/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"}