{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T19:12:25Z","timestamp":1649099545992},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2019,10,18]],"date-time":"2019-10-18T00:00:00Z","timestamp":1571356800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The hedgehog <jats:italic>H<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> is a 3-uniform hypergraph on vertices <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548319000312_inline1\" \/><jats:tex-math>$1, \\ldots ,t + \\left({\\matrix{t \\cr 2}}\\right)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that, for any pair (<jats:italic>i<\/jats:italic>, <jats:italic>j<\/jats:italic>) with 1 \u2264 <jats:italic>i<\/jats:italic> &lt; <jats:italic>j<\/jats:italic> \u2264 <jats:italic>t<\/jats:italic>, there exists a unique vertex <jats:italic>k<\/jats:italic> &gt; <jats:italic>t<\/jats:italic> such that {<jats:italic>i<\/jats:italic>, <jats:italic>j<\/jats:italic>, <jats:italic>k<\/jats:italic>} is an edge. Conlon, Fox and R\u00f6dl proved that the two-colour Ramsey number of the hedgehog grows polynomially in the number of its vertices, while the four-colour Ramsey number grows exponentially in the square root of the number of vertices. They asked whether the two-colour Ramsey number of the hedgehog <jats:italic>H<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> is nearly linear in the number of its vertices. We answer this question affirmatively, proving that <jats:italic>r<\/jats:italic>(<jats:italic>H<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub>) = <jats:italic>O<\/jats:italic>(<jats:italic>t<\/jats:italic><jats:sup>2<\/jats:sup> ln <jats:italic>t<\/jats:italic>).<\/jats:p>","DOI":"10.1017\/s0963548319000312","type":"journal-article","created":{"date-parts":[[2019,10,18]],"date-time":"2019-10-18T02:18:07Z","timestamp":1571365087000},"page":"101-112","source":"Crossref","is-referenced-by-count":0,"title":["On Ramsey numbers of hedgehogs"],"prefix":"10.1017","volume":"29","author":[{"given":"Jacob","family":"Fox","sequence":"first","affiliation":[]},{"given":"Ray","family":"Li","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,10,18]]},"reference":[{"key":"S0963548319000312_ref12","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2017.185.3.2"},{"key":"S0963548319000312_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.12.007"},{"key":"S0963548319000312_ref9","volume-title":"Ramsey Theory","author":"Graham","year":"1990"},{"key":"S0963548319000312_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.03.004"},{"key":"S0963548319000312_ref7","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.417"},{"key":"S0963548319000312_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01886396"},{"key":"S0963548319000312_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781316106853.003"},{"key":"S0963548319000312_ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-09-00645-6"},{"key":"S0963548319000312_ref2","unstructured":"[2] Burr, S. A. and Erd\u00f6s, P. (1975) On the magnitude of generalized Ramsey numbers for graphs. In Infinite and Finite Sets, Vol. 1 (Keszthely, 1973), Vol. 10 of Colloq. Math. Soc. J\u00e1nos Bolyai, pp. 214\u2013240, North-Holland."},{"key":"S0963548319000312_ref3","doi-asserted-by":"publisher","DOI":"10.4310\/JOC.2017.v8.n3.a4"},{"key":"S0963548319000312_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548303005728"},{"key":"S0963548319000312_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548303005741"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548319000312","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,14]],"date-time":"2020-01-14T05:57:04Z","timestamp":1578981424000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548319000312\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,18]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["S0963548319000312"],"URL":"https:\/\/doi.org\/10.1017\/s0963548319000312","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,18]]}}}