{"paper":{"title":"$C_{2k}$-saturated graphs with no short odd cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons","submitted_at":"2018-10-13T00:45:26Z","abstract_excerpt":"The saturation number of a graph $F$, written $\\textup{sat}(n,F)$, is the minimum number of edges in an $n$-vertex $F$-saturated graph. One of the earliest results on saturation numbers is due to Erd\\H{o}s, Hajnal, and Moon who determined $\\textup{sat}(n,K_r)$ for all $r \\geq 3$. Since then, saturation numbers of various graphs and hypergraphs have been studied. Motivated by Alon and Shikhelman's generalized Tur\\'an function, Kritschgau et.\\ al.\\ defined $\\textup{sat}(n,H,F)$ to be the minimum number of copies of $H$ in an $n$-vertex $F$-saturated graph. They proved, among other things, that $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05772","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":""},"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"}