{"paper":{"title":"Sidon sets and $C_4$-saturated graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos Alberto Trujillo, David Fernando Daza, Fenando Andr\\'es Benavides","submitted_at":"2018-10-11T21:38:06Z","abstract_excerpt":"The problem of determining the Tur\\'an number of $C_4$ is a well studied problem that dates back to a paper of Erd\\\"os from 1938. It is known that Sidon sets can be used to construct $C_4$-free graphs. If $\\A$ is a Sidon set in the abelian group $X$, the sum graph $G_{X, \\A}$ with vertex set $X$ and edges set $E=\\{\\{x, y\\}:x\\neq y, x+y\\in \\A\\}$ is $C_4$-free. Using the sum graph of a Sidon set of type Singer we verify a conjecture of Erd\\\"os and Simonovits concerning the number of copies of $C_4$ in a graph with $ex(q^2+q+1, C_4)+1$ edges. Further, we give a sufficient condition for the sum gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05262","kind":"arxiv","version":6},"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"}