{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:45:23Z","timestamp":1787323523346,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00c3\u00adfico e Tecnol\u00c3\u00b3gico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We say that a graph $G$ is Ramsey for $H_1$ versus $H_2$ and write $G \\to (H_1,H_2)$ if every red-blue coloring of the edges of $G$ contains either a red copy of $H_1$ or a blue copy of $H_2$. In this paper we study the threshold for the event that the Erd\u00f6s--R\u00e9nyi random graph $G(N,p)$ is Ramsey for a clique versus a path. We show that $G\\big( (1 + \\varepsilon) rn,p \\big) \\to (K_{r+1},P_n)$ with high probability if $p \\gg n^{-2 \/ (r + 1)}$, and $G\\big( rn + t, p \\big) \\to (K_{r+1},P_n)$ with high probability if $p \\gg n^{-2 \/ (r + 2)}$ and $t \\gg 1\/p$. Both of these results are sharp (in different ways), since with high probability $G(Cn,p) \\not\\to (K_{r+1}, P_n)$ for any constant $C&gt;0$ if $p \\ll n^{-2\/(r + 1)}$, and $G(rn + t, p) \\not\\to (K_{r+1}, P_n)$ if $t \\ll 1\/p$, for any $0&lt;p \\le 1$.<\/jats:p>","DOI":"10.1137\/19m1285093","type":"journal-article","created":{"date-parts":[[2021,9,23]],"date-time":"2021-09-23T10:51:34Z","timestamp":1632394294000},"page":"2210-2222","source":"Crossref","is-referenced-by-count":6,"title":["Ramsey Goodness of Clique Versus Paths in Random Graphs"],"prefix":"10.1137","volume":"35","author":[{"given":"Luiz","family":"Moreira","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,9,23]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-013-2778-4"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2014-00816-X"},{"key":"atypb4","first-page":"3045","volume":"3","author":"Balogh J.","year":"2018","journal-title":"Rio de Janeiro"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070115"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.10.002"},{"key":"atypb7","unstructured":"S. Berger, Y. Kohayakawa, G. S. Maesaka, T. Martins, W. Mendonca, G. O. Mota, and O. Parczyk,\n                      The Size-Ramsey Number of Powers of Bounded Degree Trees\n                      , preprint,arXiv:1907.03466."},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"B. Bollob\u00e1s,\n                      Random Graphs\n                      , 2nd ed., Cambridge University Press, Cambridge, UK, 2001.","DOI":"10.1017\/CBO9780511814068"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070106"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010118"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22432"},{"key":"atypb12","first-page":"49","volume":"424","author":"Conlon D.","year":"2015","journal-title":"Surv. Combin."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-014-1120-1"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1017\/S096354831400056X"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/16M1069717"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579174"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579245"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788087"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/jdu004"},{"key":"atypb20","first-page":"227","volume":"327","author":"Gerke S.","year":"2005","journal-title":"Surv. Combin."},{"key":"atypb21","unstructured":"J. Han, M. Jenssen, Y. Kohayakawa, G. O. Mota, and B. Roberts,\n                      The Multicolour Size-Ramsey Number of Powers of Paths\n                      , preprint,arXiv:1811.00844."},{"key":"atypb22","unstructured":"N. Kamcev, A. Liebenau, D. R. Wood, and L. Yepremyan,\n                      The Size Ramsey Number of Graphs with Bounded Treewidth\n                      , preprint,arXiv:1906.09185."},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"M. Krivelevich,\n                      Long paths and Hamiltonicity in random graphs\n                      , in Random Graphs, Geometry and Asymptotic Structure, London Mathematical Society Student Texts, Cambridge University Press, 2016, pp. 4-27.","DOI":"10.1017\/CBO9781316479988.002"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199710)11:3<245::AID-RSA3>3.0.CO;2-0"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20470"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548315000279"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(92)90006-J"},{"key":"atypb28","unstructured":"F. Mousset, R. Nenadov, and W. Samotij,\n                      Towards the Kohayakawa-Kreuter Conjecture on Asymmetric Ramsey Properties\n                      , preprint,arXiv:1808.05070."},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548314000832"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-009-2409-2"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2016.06.009"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90068-6"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.2307\/2152833"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-014-0562-8"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1285093","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:07:29Z","timestamp":1787321249000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1285093"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/19M1285093"],"URL":"https:\/\/doi.org\/10.1137\/19m1285093","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}