{"paper":{"title":"Erdos-Gallai Stability Theorem for Linear Forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ming-Zhu Chen, Xiao-Dong Zhang","submitted_at":"2019-08-02T00:20:51Z","abstract_excerpt":"The Erd\\H{o}s-Gallai Theorem states that every graph of average degree more than $l-2$ contains a path of order $l$ for $l\\ge 2$. In this paper, we obtain a stability version of the Erd\\H{o}s-Gallai Theorem in terms of minimum degree. Let $G$ be a connected graph of order $n$ and $F=(\\bigcup_{i=1}^kP_{2a_i})\\bigcup(\\bigcup_{i=1}^lP_{2b_i+1})$ be $k+l$ disjoint paths of order $2a_1, \\ldots, 2a_{k}, 2b_1+1, \\ldots, 2b_l+1,$ respectively, where $k\\ge 0$, $0\\le l\\le 2$, and $k+l\\geq 2$. If the minimum degree $\\delta(G)\\ge \\sum_{i=1}^ka_i+\\sum_{i=1}^lb_i-1$, then $F\\subseteq G$ except several class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00665","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00665/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}