{"paper":{"title":"Tur\\'an numbers for disjoint paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Long-tu Yuan, Xiao-Dong Zhang","submitted_at":"2016-11-03T12:38:35Z","abstract_excerpt":"The Tur\\'{a}n number of a graph $H$, $ex(n,H)$, is the maximum number of edges in any graph of order $n$ which does not contain $H$ as a subgraph. Lidick\\'{y}, Liu and Palmer determined $ex(n, F_m)$ for $n$ sufficiently large and proved that the extremal graph is unique, where $F_m$ is disjoint paths of $P_{k_1}, \\ldots, P_{k_m}$ [Lidick\\'{y},B., Liu,H. and Palmer,C. (2013). On the Tur\\'{a}n number of forests. Electron. J. Combin. 20(2) Paper 62, 13 pp]. In this paper, by mean of a different approach, we determine $ex(n, F_m)$ for all integers $n$ with minor conditions, which extends their par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00981","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"}