{"paper":{"title":"Chv\\'{a}tal-type results for degree sequence Ramsey numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Reiniger, Christopher Cox, Michael Ferrara, Ryan M. Martin","submitted_at":"2015-10-16T11:32:11Z","abstract_excerpt":"A sequence of nonnegative integers $\\pi =(d_1,d_2,...,d_n)$ is graphic if there is a (simple) graph $G$ of order $n$ having degree sequence $\\pi$. In this case, $G$ is said to realize or be a realization of $\\pi$. 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.\n  In this paper, we consider a degree sequence analogue to classical graph Ramsey numbers. For graphs $H_1$ and $H_2$, the potential-Ramsey number $r_{pot}(H_1,H_2)$ is the minimum integer $N$ such that for any $N$-term graphic sequence $\\pi$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04843","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"}