{"paper":{"title":"On the Ramsey number of a graph obtained by attaching a pendant to a path with length 1 modulo 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gabriel Razgon","submitted_at":"2026-07-21T20:13:46Z","abstract_excerpt":"In this paper, for odd $n$, we consider the graph $T_n$ with vertex set $\\{x_1,....,x_n,x_{n+1}\\}$ and edge set $\\{x_{1}x_{2},x_{2}x_{3},...,x_{n-1}x_{n}\\} \\cup \\{x_{\\frac{n+1}{2}}x_{n+1}\\}$ and prove that the Ramsey number $R(T_n,T_n)$ is equal to $\\frac{3n+1}{2}$ for $n \\in [1]_{4}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19554","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/2607.19554/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"}