{"publisher":"Springer","article_type":"original","type":"journal_article","date_published":"2020-07-01T00:00:00Z","oa_version":"Preprint","abstract":[{"text":"How long a monotone path can one always find in any edge-ordering of the complete graph Kn? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n2/3-o(1). In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length n1-o(1).","lang":"eng"}],"oa":1,"title":"Nearly-linear monotone paths in edge-ordered graphs","article_processing_charge":"No","language":[{"iso":"eng"}],"date_created":"2021-06-21T13:24:35Z","publication_identifier":{"issn":["0021-2172"],"eissn":["1565-8511"]},"intvolume":"       238","day":"01","issue":"2","page":"663-685","citation":{"short":"M. Bucić, M.A. Kwan, A. Pokrovskiy, B. Sudakov, T. Tran, A.Z. Wagner, Israel Journal of Mathematics 238 (2020) 663–685.","ieee":"M. Bucić, M. A. Kwan, A. Pokrovskiy, B. Sudakov, T. Tran, and A. Z. Wagner, “Nearly-linear monotone paths in edge-ordered graphs,” <i>Israel Journal of Mathematics</i>, vol. 238, no. 2. Springer, pp. 663–685, 2020.","ama":"Bucić M, Kwan MA, Pokrovskiy A, Sudakov B, Tran T, Wagner AZ. Nearly-linear monotone paths in edge-ordered graphs. <i>Israel Journal of Mathematics</i>. 2020;238(2):663-685. doi:<a href=\"https://doi.org/10.1007/s11856-020-2035-7\">10.1007/s11856-020-2035-7</a>","chicago":"Bucić, Matija, Matthew Alan Kwan, Alexey Pokrovskiy, Benny Sudakov, Tuan Tran, and Adam Zsolt Wagner. “Nearly-Linear Monotone Paths in Edge-Ordered Graphs.” <i>Israel Journal of Mathematics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s11856-020-2035-7\">https://doi.org/10.1007/s11856-020-2035-7</a>.","apa":"Bucić, M., Kwan, M. A., Pokrovskiy, A., Sudakov, B., Tran, T., &#38; Wagner, A. Z. (2020). Nearly-linear monotone paths in edge-ordered graphs. <i>Israel Journal of Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11856-020-2035-7\">https://doi.org/10.1007/s11856-020-2035-7</a>","mla":"Bucić, Matija, et al. “Nearly-Linear Monotone Paths in Edge-Ordered Graphs.” <i>Israel Journal of Mathematics</i>, vol. 238, no. 2, Springer, 2020, pp. 663–85, doi:<a href=\"https://doi.org/10.1007/s11856-020-2035-7\">10.1007/s11856-020-2035-7</a>.","ista":"Bucić M, Kwan MA, Pokrovskiy A, Sudakov B, Tran T, Wagner AZ. 2020. Nearly-linear monotone paths in edge-ordered graphs. Israel Journal of Mathematics. 238(2), 663–685."},"publication":"Israel Journal of Mathematics","month":"07","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01468"}],"scopus_import":"1","volume":238,"extern":"1","publication_status":"published","status":"public","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","date_updated":"2023-02-23T14:01:35Z","author":[{"full_name":"Bucić, Matija","first_name":"Matija","last_name":"Bucić"},{"full_name":"Kwan, Matthew Alan","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","first_name":"Matthew Alan"},{"full_name":"Pokrovskiy, Alexey","last_name":"Pokrovskiy","first_name":"Alexey"},{"full_name":"Sudakov, Benny","first_name":"Benny","last_name":"Sudakov"},{"last_name":"Tran","first_name":"Tuan","full_name":"Tran, Tuan"},{"full_name":"Wagner, Adam Zsolt","last_name":"Wagner","first_name":"Adam Zsolt"}],"external_id":{"arxiv":["1809.01468"]},"quality_controlled":"1","doi":"10.1007/s11856-020-2035-7","_id":"9578","year":"2020"}