{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T02:02:06Z","timestamp":1648605726883},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5034,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1994,12]]},"abstract":"<jats:p>In [11] it is shown that the theory of almost all graphs is first-order complete. Furthermore, in [3] a collection of first-order axioms are given from which any first-order property or its negation can be deduced. Here we show that almost all Steinhaus graphs satisfy the axioms of almost all graphs and conclude that a first-order property is true for almost all graphs if and only if it is true for almost all Steinhaus graphs. We also show that certain classes of subgraphs of vertex transitive graphs are first-order complete. Finally, we give a new class of higher-order axioms from which it follows that large subgraphs of specified type exist in almost all graphs.<\/jats:p>","DOI":"10.1017\/s0963548300001346","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:15:47Z","timestamp":1221218147000},"page":"435-454","source":"Crossref","is-referenced-by-count":1,"title":["Properties of Classes of Random Graphs"],"prefix":"10.1017","volume":"3","author":[{"given":"Neal","family":"Brand","sequence":"first","affiliation":[]},{"given":"Steve","family":"Jackson","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300001346_ref002","volume-title":"Probability and Measure","author":"Billingsley","year":"1979"},{"key":"S0963548300001346_ref001","first-page":"45","article-title":"Regular Steinhaus graphs","volume":"66","author":"Bailey","year":"1988","journal-title":"Congressus Numerantium"},{"key":"S0963548300001346_ref004","volume-title":"Random Graphs","author":"Bollob\u00e1s","year":"1985"},{"key":"S0963548300001346_ref005","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190160304"},{"key":"S0963548300001346_ref014","volume-title":"One Hundred Problems in Elementary Mathematics","author":"Steinhaus","year":"1963"},{"key":"S0963548300001346_ref011","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200051756"},{"key":"S0963548300001346_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90064-6"},{"key":"S0963548300001346_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(72)90039-8"},{"key":"S0963548300001346_ref008","first-page":"7","article-title":"Distances and diameters in Steinhaus graphs","volume":"76","author":"Brigham","year":"1990","journal-title":"Congressus Numerantium"},{"key":"S0963548300001346_ref013","volume-title":"Fundamentals of Algorithms","volume":"1","author":"Knuth","year":"1973"},{"key":"S0963548300001346_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(93)90036-N"},{"key":"S0963548300001346_ref010","first-page":"41","article-title":"Small cycles in Steinhaus graphs","volume":"70","author":"Dymacek","year":"1990","journal-title":"Congressus Numerantium"},{"key":"S0963548300001346_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190030305"},{"key":"S0963548300001346_ref007","unstructured":"[7] Brigham R. C. , Deo N. and Dutton R. D. (preprint) Some properties of Steinhaus graphs."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300001346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T23:44:02Z","timestamp":1557877442000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300001346\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,12]]}},"alternative-id":["S0963548300001346"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300001346","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,12]]}}}