{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T13:38:22Z","timestamp":1760621902988,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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\u0151s and Galvin, and of DeBiasio and McKenney.<\/jats:p>","DOI":"10.37236\/7758","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:03:15Z","timestamp":1578668595000},"source":"Crossref","is-referenced-by-count":4,"title":["Density of Monochromatic Infinite Paths"],"prefix":"10.37236","volume":"25","author":[{"given":"Allan","family":"Lo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicol\u00e1s","family":"Sanhueza-Matamala","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghui","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,11,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p29\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:21:40Z","timestamp":1579234900000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,2]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7758","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,11,2]]},"article-number":"P4.29"}}