{"paper":{"title":"Short proof of two cases of Chv\\'atal's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francisco Santos, Jonathan Spreer, Jorge Olarte","submitted_at":"2018-04-10T17:49:56Z","abstract_excerpt":"In 1974 Chv\\'atal conjectured that no intersecting family $\\mathcal{F}$ in a downset can be larger than the largest star. In the same year Kleitman and Magnanti proved the conjecture when $\\mathcal{F}$ is contained in the union of two stars, and Sterboul when $\\operatorname{rank}(\\mathcal{F})\\le 3$. We give short self-contained proofs of these two statements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03646","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":""},"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"}