{"paper":{"title":"An Ore-type Alon-Yuster Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanghui Wang, Lin-Peng Zhang, Yilin Guo, Yuping Gao","submitted_at":"2026-05-21T14:35:30Z","abstract_excerpt":"A graph $G$ admits an $H$-tiling if it contains a collection of vertex-disjoint copies of $H$. In this paper, we confirm a conjecture proposed by K\\\"{u}hn, Osthus, and Treglown by showing that for any given graph $H$, there exists a constant $C(H)$ such that the following holds. If $G$ is a sufficiently large $n$-vertex graph satisfying $d(x) + d(y) \\geq 2\\left(1 - 1/\\chi_{\\text{cr}}(H)\\right)n$ for all nonadjacent vertices $x, y \\in V(G)$, then $G$ contains an $H$-tiling covering all but at most $C(H)$ vertices. Here $\\chi_{\\text{cr}}(H)$ denotes the critical chromatic number of $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22553","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/2605.22553/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"}