{"paper":{"title":"Book Ramsey numbers via algebraic constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lulu Dai, Qizhong Lin","submitted_at":"2026-06-05T12:26:22Z","abstract_excerpt":"Let $B_n$ denote the book graph consisting of $n$ triangles sharing a common edge. Few exact values of $R(B_n,B_n)$ have been obtained since Rousseau and Sheehan (1978) proved, using Paley graphs, $R(B_n, B_n) = 4n + 2$ whenever $4n+1$ is a prime power.\n  In this paper, we obtain $R(B_n,B_n)=4n+1$ for infinitely many $n$ by constructing new families of strongly regular graphs. Moreover, we prove that $R(B_{n-2},B_n)\\le 4n-3$ for every $n\\ge 3$ with $n\\ne 6$, removing the original condition $n\\equiv 2\\pmod 3$ due to Rousseau and Sheehan. In particular, if there exists a symmetric Hadamard matri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07214","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/2606.07214/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"}