{"paper":{"title":"On the maximal anti-Ramsey problem of Burr, Erd\\H{o}s, Graham, and S\\'{o}s for $P_4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zixuan Yang","submitted_at":"2026-07-07T06:47:41Z","abstract_excerpt":"Given a graph $L$, the maximal anti-Ramsey function $\\chiS(n,e,L)$ denotes the minimum integer $\\chiS$ for which there exists an $n$-vertex graph $G$ with at least $e$ edges admitting an edge-coloring with $\\chiS$ colors in which each copy of $L$ in $G$ is rainbow. In 1989, Burr, Erd\\H{o}s, Graham, and S\\'{o}s posed the following problem: Is it true that for all $\\epsilon>0$, there exists $c(\\epsilon)>0$ such that for all sufficiently large $n$, $\n\\chiS\\left(n,\\binom{n}{2}-\\lfloor n^{2-\\epsilon}\\rfloor,P_4\\right)>c(\\epsilon)n^2. $\nVery recently, Li, Ning, and Xie gave a negative answer to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05896","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/2607.05896/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"}