{"paper":{"title":"Ordered Ramsey numbers of powers of paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ant\\'onio Gir\\~ao, Barnab\\'as Janzer, Oliver Janzer","submitted_at":"2024-01-04T17:00:01Z","abstract_excerpt":"Given two vertex-ordered graphs $G$ and $H$, the ordered Ramsey number $R_<(G,H)$ is the smallest $N$ such that whenever the edges of a vertex-ordered complete graph $K_N$ are red/blue-coloured, then there is a red (ordered) copy of $G$ or a blue (ordered) copy of $H$. Let $P_n^t$ denote the $t$-th power of a monotone path on $n$ vertices. The ordered Ramsey numbers of powers of paths have been extensively studied. We prove that there exists an absolute constant $C$ such that $R_<(K_s,P_n^t)\\leq R(K_s,K_t)^{C} \\cdot n$ holds for all $s,t,n$, which is tight up to the value of $C$. As a corollar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.02360","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.02360/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"}