[{"page":"67-111","issue":"1","day":"01","publication":"Israel Journal of Mathematics","month":"08","_id":"9580","date_updated":"2021-08-09T12:25:11Z","type":"journal_article","article_processing_charge":"No","status":"public","external_id":{"arxiv":["1803.08462"]},"main_file_link":[{"url":"https://arxiv.org/abs/1803.08462","open_access":"1"}],"citation":{"chicago":"Conlon, David, Jacob Fox, Matthew Alan Kwan, and Benny Sudakov. “Hypergraph Cuts above the Average.” *Israel Journal of Mathematics*. Springer, 2019. https://doi.org/10.1007/s11856-019-1897-z.","ama":"Conlon D, Fox J, Kwan MA, Sudakov B. Hypergraph cuts above the average. *Israel Journal of Mathematics*. 2019;233(1):67-111. doi:10.1007/s11856-019-1897-z","mla":"Conlon, David, et al. “Hypergraph Cuts above the Average.” *Israel Journal of Mathematics*, vol. 233, no. 1, Springer, 2019, pp. 67–111, doi:10.1007/s11856-019-1897-z.","short":"D. Conlon, J. Fox, M.A. Kwan, B. Sudakov, Israel Journal of Mathematics 233 (2019) 67–111.","ieee":"D. Conlon, J. Fox, M. A. Kwan, and B. Sudakov, “Hypergraph cuts above the average,” *Israel Journal of Mathematics*, vol. 233, no. 1. Springer, pp. 67–111, 2019.","ista":"Conlon D, Fox J, Kwan MA, Sudakov B. 2019. Hypergraph cuts above the average. Israel Journal of Mathematics. 233(1), 67–111.","apa":"Conlon, D., Fox, J., Kwan, M. A., & Sudakov, B. (2019). Hypergraph cuts above the average. *Israel Journal of Mathematics*. Springer. https://doi.org/10.1007/s11856-019-1897-z"},"article_type":"original","doi":"10.1007/s11856-019-1897-z","abstract":[{"lang":"eng","text":"An r-cut of a k-uniform hypergraph H is a partition of the vertex set of H into r parts and the size of the cut is the number of edges which have a vertex in each part. A classical result of Edwards says that every m-edge graph has a 2-cut of size m/2+Ω)(m−−√) and this is best possible. That is, there exist cuts which exceed the expected size of a random cut by some multiple of the standard deviation. We study analogues of this and related results in hypergraphs. First, we observe that similarly to graphs, every m-edge k-uniform hypergraph has an r-cut whose size is Ω(m−−√) larger than the expected size of a random r-cut. Moreover, in the case where k = 3 and r = 2 this bound is best possible and is attained by Steiner triple systems. Surprisingly, for all other cases (that is, if k ≥ 4 or r ≥ 3), we show that every m-edge k-uniform hypergraph has an r-cut whose size is Ω(m5/9) larger than the expected size of a random r-cut. This is a significant difference in behaviour, since the amount by which the size of the largest cut exceeds the expected size of a random cut is now considerably larger than the standard deviation."}],"date_published":"2019-08-01T00:00:00Z","publisher":"Springer","intvolume":" 233","oa":1,"author":[{"first_name":"David","full_name":"Conlon, David","last_name":"Conlon"},{"last_name":"Fox","full_name":"Fox, Jacob","first_name":"Jacob"},{"full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","first_name":"Matthew Alan"},{"full_name":"Sudakov, Benny","last_name":"Sudakov","first_name":"Benny"}],"date_created":"2021-06-21T13:36:02Z","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","oa_version":"Preprint","extern":"1","year":"2019","title":"Hypergraph cuts above the average","quality_controlled":"1","scopus_import":"1","publication_status":"published","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0021-2172"],"eissn":["1565-8511"]},"volume":233}]