{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:08:37Z","timestamp":1777442917019,"version":"3.51.4"},"reference-count":24,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5031,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1993,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A classical result of R\u00f6dl (in <jats:italic>Graphs, Hypergraphs and Block Systems<\/jats:italic>, 1976, pp. 211 to 220) says that for any acyclic digraph <jats:italic>D<\/jats:italic> there is a graph <jats:italic>G<\/jats:italic> = <jats:italic>G(D)<\/jats:italic> such that every acyclic orientation of <jats:italic>G<\/jats:italic> contains an induced copy of <jats:italic>D<\/jats:italic>. A recent result of R\u00f6dl and Winkler (<jats:italic>SIAM J. Discrete Math.<\/jats:italic>, <jats:bold>2<\/jats:bold>: 402\u2013406, 1989) implies that there is such a graph <jats:italic>G<\/jats:italic> of order <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>3<\/jats:sup> (log <jats:italic>n<\/jats:italic>)<jats:sup>2<\/jats:sup>), where <jats:italic>n<\/jats:italic> = |<jats:italic>D<\/jats:italic>| is the order of <jats:italic>D<\/jats:italic>. Here we show by probabilistic means that almost every graph <jats:italic>G<jats:sub>n<\/jats:sub><\/jats:italic> of order [(4\/9)<jats:italic>n<\/jats:italic>2<jats:sup><jats:italic>n<\/jats:italic>\/2<\/jats:sup>] has the property that every acyclic orientation of <jats:italic>G<\/jats:italic><jats:sub>n<\/jats:sub> contains an induced copy of <jats:italic>every<\/jats:italic> acyclic digraph on <jats:italic>n<\/jats:italic> vertices. We also show that the order of any such graph <jats:italic>G<jats:sub>n<\/jats:sub><\/jats:italic> has to be greater than (1\/10)<jats:italic>n<\/jats:italic>2<jats:sup><jats:italic>n<\/jats:italic>\/2<\/jats:sup>. Thus our results are essentially best possible. Moreover, we show that there are Paley graphs of order <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup>4<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>) having the property above. We also consider some problems raised by Cochand and Duchet (<jats:italic>Irregularities of Partitions<\/jats:italic>, Springer\u2010Verlag, Berlin, 1989, pp. 39\u201346.) on related topics. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/rsa.3240040403","type":"journal-article","created":{"date-parts":[[2007,5,31]],"date-time":"2007-05-31T17:48:42Z","timestamp":1180633722000},"page":"413-428","source":"Crossref","is-referenced-by-count":10,"title":["Ramsey properties of orientations of graphs"],"prefix":"10.1002","volume":"4","author":[{"given":"G. R.","family":"Brightwell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"Kohayakawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00341633"},{"key":"e_1_2_1_3_2","unstructured":"N.Alon B.Bollob\u00e1s G. R.Brightwell andS.Janson Linear extensions of a random partial order submitted."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/0605049"},{"key":"e_1_2_1_5_2","first-page":"67","article-title":"Geodesics in oriented graphs","volume":"20","author":"Bollob\u00e1s B.","year":"1984","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_6_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_7_2","series-title":"Proc. Colloq. Math. Soc. J. Bolyai 52","volume-title":"Combinatorics","author":"Bollob\u00e1s B.","year":"1988"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02122551"},{"key":"e_1_2_1_9_2","first-page":"1","volume-title":"Random Graphs '87","author":"Bollob\u00e1s B.","year":"1990"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1090\/psapm\/044\/1141921"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(81)80015-7"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140408"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61324-1_3"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1959-003-9"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300003260"},{"key":"e_1_2_1_16_2","first-page":"115","volume-title":"Theory of Graphs","author":"Gallai T.","year":"1968"},{"key":"e_1_2_1_17_2","volume-title":"An Introduction to the Theory of Numbers","author":"Hardy G. H.","year":"1960"},{"key":"e_1_2_1_18_2","first-page":"148","volume-title":"London Mathematical Society Lecture Notes Series","author":"McDiarmid C. J. H.","year":"1989"},{"key":"e_1_2_1_19_2","article-title":"On ordered graphs and graph orderings","author":"Ne\u0161et\u0159il J.","journal-title":"Discrete Math."},{"key":"e_1_2_1_20_2","first-page":"405","volume-title":"Recent Advances in Graph Theory","author":"Ne\u0161et\u0159il J.","year":"1975"},{"key":"e_1_2_1_21_2","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1090\/S0002-9939-1978-0507350-7","article-title":"A probabilistic graph theoretical method","volume":"72","author":"Ne\u0161et\u0159il J.","year":"1978","journal-title":"Proc. Am. Math. Soc."},{"key":"e_1_2_1_22_2","unstructured":"V.R\u00f6dl A generalization of Ramsey theorem inGraphs Hypergraphs and Block Systems Zielona Gora 1976pp.211\u2013220."},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1137\/0402035"},{"key":"e_1_2_1_24_2","first-page":"211","volume-title":"Annals of Discrete Mathematics","author":"Rosenfeld M.","year":"1984"},{"key":"e_1_2_1_25_2","series-title":"London Mathematical Society Lecture Notes Series","first-page":"173","volume-title":"Random graphs, strongly regular graphs and pseudo\u2010random graphs, in Surveys in Combinatorics 1987, Invited Papers at the 11th British Combinatorial Conference","author":"Thomason A. 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