{"paper":{"title":"On the approximate shape of degree sequences that are not potentially $H$-graphic","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":"2013-03-22T14:17:03Z","abstract_excerpt":"A sequence of nonnegative integers $\\pi$ is {\\it graphic} if it is the degree sequence of some graph $G$. In this case we say that $G$ is a \\textit{realization} of $\\pi$, and we write $\\pi=\\pi(G)$. A graphic sequence $\\pi$ is {\\it potentially $H$-graphic} if there is a realization of $\\pi$ that contains $H$ as a subgraph.\n  Given nonincreasing graphic sequences $\\pi_1=(d_1,\\ldots,d_n)$ and $\\pi_2 = (s_1,\\ldots,s_n)$, we say that $\\pi_1$ {\\it majorizes} $\\pi_2$ if $d_i \\geq s_i$ for all $i$, $1 \\leq i \\leq n$. In 1970, Erd\\H{o}s showed that for any $K_{r+1}$-free graph $H$, there exists an $r$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5622","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"}