{"paper":{"title":"Chromatic Ramsey numbers and two-color Tur\\'{a}n densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dingyuan Liu, Maria Axenovich, Simon Gaa","submitted_at":"2024-09-11T18:00:27Z","abstract_excerpt":"Given a graph $G$, its $2$-color Tur\\'{a}n number $\\mathrm{ex}^{(2)}(n,G)$ is the maximum number of edges in an $n$-vertex graph, such that the edges can be colored with two colors avoiding a monochromatic copy of $G$. Let $\\pi^{(2)}(G)=\\lim_{n\\to\\infty}\\mathrm{ex}^{(2)}(n,G)/\\binom{n}{2}$ be the $2$-color Tur\\'{a}n density of $G$. What real numbers in the interval $(0,1)$ are realized as the $2$-color Tur\\'{a}n density of some graph? It is known that $\\pi^{(2)}(G)=1-(R_{\\chi}(G)-1)^{-1}$, where $R_{\\chi}(G)$ is the chromatic Ramsey number of $G$. Burr, Erd\\H{o}s, and Lov\\'{a}sz showed that $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.07535","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.07535/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"}