{"paper":{"title":"Finding irregular subgraphs via local adjustments","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma, Shengjie Xie","submitted_at":"2024-06-09T07:16:07Z","abstract_excerpt":"For a graph $H$, let $m(H,k)$ denote the number of vertices of degree $k$ in $H$. A conjecture of Alon and Wei states that for any $d\\geq 3$, every $n$-vertex $d$-regular graph contains a spanning subgraph $H$ satisfying $|m(H,k)-\\frac{n}{d+1}|\\leq 2$ for every $0\\leq k \\leq d$. This holds easily when $d\\leq 2$. An asymptotic version of this conjecture was initially established by Frieze, Gould, Karo\\'nski and Pfender, subsequently improved by Alon and Wei, and most recently enhanced by Fox, Luo and Pham, approaching its complete range. All of these approaches relied on probabilistic methods.\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.05675","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/2406.05675/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"}