{"paper":{"title":"On the size-Ramsey number of tight paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Linyuan Lu, Zhiyu Wang","submitted_at":"2017-12-08T19:04:15Z","abstract_excerpt":"For any $r\\geq 2$ and $k\\geq 3$, the $r$-color size-Ramsey number $\\hat R(\\mathcal{G},r)$ of a $k$-uniform hypergraph $\\mathcal{G}$ is the smallest integer $m$ such that there exists a $k$-uniform hypergraph $\\mathcal{H}$ on $m$ edges such that any coloring of the edges of $\\mathcal{H}$ with $r$ colors yields a monochromatic copy of $\\mathcal{G}$. Let $\\mathcal{P}_{n,k-1}^{(k)}$ denote the $k$-uniform tight path on $n$ vertices. Dudek, Fleur, Mubayi and R\\H{o}dl showed that the size-Ramsey number of tight paths $\\hat R(\\mathcal{P}_{n,k-1}^{(k)}, 2) = O(n^{k-1-\\alpha} (\\log n)^{1+\\alpha})$ wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03247","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":""},"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"}