{"paper":{"title":"Stability of the potential function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Erbes, Michael Ferrara, Paul Wenger, Ryan R. Martin","submitted_at":"2018-10-17T21:01:05Z","abstract_excerpt":"A graphic sequence $\\pi$ is potentially $H$-graphic if there is some realization of $\\pi$ that contains $H$ as a subgraph. The Erd\\H{o}s-Jacobson-Lehel problem asks to determine $\\sigma(H,n)$, the minimum even integer such that any $n$-term graphic sequence $\\pi$ with sum at least $\\sigma(H,n)$ is potentially $H$-graphic. The parameter $\\sigma(H,n)$ is known as the potential function of $H$, and can be viewed as a degree sequence variant of the classical extremal function ${\\rm ex}(n,H)$. Recently, Ferrara, LeSaulnier, Moffatt and Wenger [On the sum necessary to ensure that a degree sequence i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07794","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"}