{"paper":{"title":"Density of monochromatic infinite paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Allan Lo, Guanghui Wang, Nicol\\'as Sanhueza-Matamala","submitted_at":"2018-08-01T15:55:21Z","abstract_excerpt":"For any subset $A \\subseteq \\mathbb{N}$, we define its upper density to be $\\limsup_{ n \\rightarrow \\infty } |A \\cap \\{ 1, \\dotsc, n \\}| / n$. We prove that every $2$-edge-colouring of the complete graph on $\\mathbb{N}$ contains a monochromatic infinite path, whose vertex set has upper density at least $(9 + \\sqrt{17})/16 \\approx 0.82019$. This improves on results of Erd\\H{o}s and Galvin, and of DeBiasio and McKenney."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00389","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"}