{"paper":{"title":"On the size-Ramsey number of cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Farideh Khoeini, Gholam Reza Omidi, Ramin Javadi","submitted_at":"2017-01-25T15:13:15Z","abstract_excerpt":"For given graphs $G_1,\\ldots,G_k$, the size-Ramsey number $\\hat{R}(G_1,\\ldots,G_k)$ is the smallest integer $m$ for which there exists a graph $H$ on $m$ edges such that in every $k$-edge coloring of $H$ with colors $1,\\ldots,k$, $ H $ contains a monochromatic copy of $G_i$ of color $i$ for some $1\\leq i\\leq k$. We denote $\\hat{R}(G_1,\\ldots,G_k)$ by $\\hat{R}_{k}(G)$ when $G_1=\\cdots=G_k=G$. Haxell, Kohayakawa and \\L{}uczak showed that the size Ramsey number of a cycle $C_n$ is linear in $n$ i.e. $\\hat{R}_{k}(C_{n})\\leq c_k n$ for some constant $c_k$. Their proof, is based on the regularity le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07348","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"}