{"paper":{"title":"Extremal $G$-free induced subgraphs of Kneser graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Taherkhani, Meysam Alishahi","submitted_at":"2018-01-11T20:06:30Z","abstract_excerpt":"The Kneser graph ${\\rm KG}_{n,k}$ is a graph whose vertex set is the family of all $k$-subsets of $[n]$ and two vertices are adjacent if their corresponding subsets are disjoint. The classical Erd\\H{o}s-Ko-Rado theorem determines the cardinality and structure of a maximum induced $K_2$-free subgraph in ${\\rm KG}_{n,k}$. As a generalization of the Erd\\H{o}s-Ko-Rado theorem, Erd\\H{o}s proposed a conjecture about the maximum order of an induced $K_{s+1}$-free subgraph of ${\\rm KG}_{n,k}$. As the best known result concerning this conjecture, Frankl [Journal of Combinatorial Theory, Series A, 2013]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03972","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"}