{"paper":{"title":"On the least size of a graph with a given degree set -- II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aditya Sahdev, Amitabha Tripathi, Jai Moondra","submitted_at":"2020-09-22T03:00:02Z","abstract_excerpt":"The degree set of a finite simple graph $G$ is the set of distinct degrees of vertices of $G$. A theorem of Kapoor, Polimeni & Wall asserts that the least order of a graph with a given degree set $\\mathscr D$ is $1+\\max \\mathscr D$. Tripathi & Vijay considered the analogous problem concerning the least size of graphs with degree set $\\mathscr D$. We expand on their results, and determine the least size of graphs with degree set $\\mathscr D$ when (i) $\\min \\mathscr D \\mid d$ for each $d \\in \\mathscr D$; (ii) $\\min \\mathscr D=2$; (iii) $\\mathscr D=\\{m,m+1,\\ldots,n\\}$. In addition, given any $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10294","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/2009.10294/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"}