{"paper":{"title":"Phase transitions of the Erd\\H{o}s-Gy\\'{a}rf\\'{a}s function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanghui Wang, Qizhong Lin, Xin Lu, Xinyu Hu","submitted_at":"2025-04-08T03:49:05Z","abstract_excerpt":"Given positive integers $p,q$. For any integer $k\\ge2$, an edge coloring of the complete $k$-graph $K_n^{(k)}$ is said to be a $(p,q)$-coloring if every copy of $K_p^{(k)}$ receives at least $q$ colors. The Erd\\H{o}s-Gy\\'{a}rf\\'{a}s function $f_k(n,p,q)$ is the minimum number of colors that are needed for $K_n^{(k)}$ to have a $(p,q)$-coloring.\n  Conlon, Fox, Lee and Sudakov (\\emph{IMRN, 2015}) conjectured that for any positive integers $p, k$ and $i$ with $k\\ge3$ and $1\\le i<k$, $f_k(n,p,{{p-i}\\choose{k-i}})=(\\log_{(i-1)}n)^{o(1)}$, where $\\log_{(i)}n$ is an iterated $i$-fold logarithm in $n$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.05647","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/2504.05647/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"}