{"paper":{"title":"On the Sum Neccesary to Ensure that a Degree Sequence is Potentially H-Graphic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Casey K. Moffatt, Michael Ferrara, Paul S. Wenger, Timothy D. LeSaulnier","submitted_at":"2012-03-20T22:22:20Z","abstract_excerpt":"A sequence of nonnegative integers \\pi =(d_1,d_2,...,d_n) is graphic if there is a (simple) graph G with degree sequence \\pi. In this case, G is said to realize or be a realization of \\pi. Degree sequence results in the literature generally fall into two classes: forcible problems, in which all realizations of a graphic sequence must have a given property, and potential problems, in which at least one realization of \\pi must have the given property.\n  Given a graph H, a graphic sequence \\pi is potentially H-graphic if there is some realization of \\pi that contains H as a subgraph. In 1991, Erd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4611","kind":"arxiv","version":2},"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"}