{"paper":{"title":"On ordered Ramsey numbers of bounded-degree graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Martin Balko, Pavel Valtr, V\\'it Jel\\'inek","submitted_at":"2016-06-17T19:12:35Z","abstract_excerpt":"An ordered graph is a pair $\\mathcal{G}=(G,\\prec)$ where $G$ is a graph and $\\prec$ is a total ordering of its vertices. The ordered Ramsey number $\\overline{R}(\\mathcal{G})$ is the minimum number $N$ such that every $2$-coloring of the edges of the ordered complete graph on $N$ vertices contains a monochromatic copy of $\\mathcal{G}$.\n  We show that for every integer $d \\geq 3$, almost every $d$-regular graph $G$ satisfies $\\overline{R}(\\mathcal{G}) \\geq \\frac{n^{3/2-1/d}}{4\\log{n}\\log{\\log{n}}}$ for every ordering $\\mathcal{G}$ of $G$. In particular, there are 3-regular graphs $G$ on $n$ vert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05628","kind":"arxiv","version":2},"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"}