{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:13:42Z","timestamp":1775837622190,"version":"3.50.1"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2015,2,24]],"date-time":"2015-02-24T00:00:00Z","timestamp":1424736000000},"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":[[2016,3]]},"abstract":"<jats:p>Ne\u0161et\u0159il and Ossona de Mendez introduced the notion of first-order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether, if (<jats:italic>G<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>)<jats:sub><jats:italic>i<\/jats:italic>\u2208\u2115<\/jats:sub> is a sequence of graphs with <jats:italic>M<\/jats:italic> being their first-order limit and <jats:italic>v<\/jats:italic> is a vertex of <jats:italic>M<\/jats:italic>, then there exists a sequence (<jats:italic>v<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>)<jats:sub><jats:italic>i<\/jats:italic>\u2208\u2115<\/jats:sub> of vertices such that the graphs <jats:italic>G<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> rooted at <jats:italic>v<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> converge to <jats:italic>M<\/jats:italic> rooted at <jats:italic>v<\/jats:italic>. We show that this holds for almost all vertices <jats:italic>v<\/jats:italic> of <jats:italic>M<\/jats:italic>, and we give an example showing that the statement need not hold for all vertices.<\/jats:p>","DOI":"10.1017\/s0963548315000048","type":"journal-article","created":{"date-parts":[[2015,2,24]],"date-time":"2015-02-24T15:17:13Z","timestamp":1424791033000},"page":"213-221","source":"Crossref","is-referenced-by-count":3,"title":["First-Order Convergence and Roots"],"prefix":"10.1017","volume":"25","author":[{"given":"DEMETRES","family":"CHRISTOFIDES","sequence":"first","affiliation":[]},{"given":"DANIEL","family":"KR\u00c1L\u2019","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,2,24]]},"reference":[{"key":"S0963548315000048_ref14","first-page":"581","article-title":"A model theory approach to structural limits, Comment","volume":"53","author":"Ne\u0161et\u0159il","year":"2012","journal-title":"Math. Univ. Carolin."},{"key":"S0963548315000048_ref11","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/060"},{"key":"S0963548315000048_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-007-2214-8"},{"key":"S0963548315000048_ref15","unstructured":"Ne\u0161et\u0159il J. and Ossona de Mendez P. A unified approach to structural limits, and limits of graphs with bounded tree-depth. arXiv:1303.6471"},{"key":"S0963548315000048_ref16","unstructured":"Ne\u0161et\u0159il J. and Ossona de Mendez P. Modeling limits in hereditary classes: Reduction and application to trees. arXiv:1312.0441"},{"key":"S0963548315000048_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-014-0258-7"},{"key":"S0963548315000048_ref3","first-page":"261","volume-title":"Proc. 38rd Annual ACM Symposium on the Theory of Computing: STOC","author":"Borgs","year":"2006"},{"key":"S0963548315000048_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v6-96"},{"key":"S0963548315000048_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v12-463"},{"key":"S0963548315000048_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.05.002"},{"key":"S0963548315000048_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14279-6"},{"key":"S0963548315000048_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2008.07.008"},{"key":"S0963548315000048_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-010-0060-7"},{"key":"S0963548315000048_ref7","volume-title":"Finite Model Theory","author":"Ebbinghaus","year":"2005"},{"key":"S0963548315000048_ref10","unstructured":"Kr\u00e1l' D. , Kupec M. and T\u016fma V. Modelings of trees. In preparation."},{"key":"S0963548315000048_ref5","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2012.176.1.2"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548315000048","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,19]],"date-time":"2019-04-19T20:52:20Z","timestamp":1555707140000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548315000048\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,24]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["S0963548315000048"],"URL":"https:\/\/doi.org\/10.1017\/s0963548315000048","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,24]]}}}