{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T17:04:22Z","timestamp":1780679062324,"version":"3.54.1"},"reference-count":24,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T00:00:00Z","timestamp":1776902400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000086","name":"National Science Foundation Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Combinatorial Theory, Series A"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.jcta.2026.106215","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T16:11:01Z","timestamp":1777997461000},"page":"106215","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Word-representation numbers of graphs: Bottlenecks and bounds"],"prefix":"10.1016","volume":"223","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3357-8944","authenticated-orcid":false,"given":"Zion","family":"Hefty","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Horn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Colby","family":"Muir","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew","family":"Owens","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.jcta.2026.106215_br0010","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1002\/jgt.20296","article-title":"On the editing distance of graphs","volume":"58","author":"Axenovich","year":"2008","journal-title":"J. Graph Theory"},{"key":"10.1016\/j.jcta.2026.106215_br0020","doi-asserted-by":"crossref","first-page":"29","DOI":"10.61091\/um122-02","article-title":"On 1-11-representability and multi-1-11-representability of graphs","volume":"122","author":"Alshammari","year":"2025","journal-title":"Util. Math."},{"key":"10.1016\/j.jcta.2026.106215_br0030","series-title":"Paul Erd\u0151s and His Mathematics","first-page":"155","article-title":"Ramsey-type theorems with forbidden subgraphs","volume":"vol. 21","author":"Alon","year":"2001"},{"issue":"1","key":"10.1016\/j.jcta.2026.106215_br0040","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1002\/rsa.20209","article-title":"What is the furthest graph from a hereditary property?","volume":"33","author":"Alon","year":"2008","journal-title":"Random Struct. Algorithms"},{"issue":"1","key":"10.1016\/j.jcta.2026.106215_br0050","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1080\/15427951.2006.10129115","article-title":"Concentration inequalities and martingale inequalities: a survey","volume":"3","author":"Chung","year":"2006","journal-title":"Internet Math."},{"issue":"3","key":"10.1016\/j.jcta.2026.106215_br0060","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1112\/plms.12504","article-title":"Erd\u0151s-Hajnal for graphs with no 5-hole","volume":"126","author":"Chudnovsky","year":"2023","journal-title":"Proc. Lond. Math. Soc. (3)"},{"key":"10.1016\/j.jcta.2026.106215_br0070","doi-asserted-by":"crossref","first-page":"600","DOI":"10.2307\/2371374","article-title":"Partially ordered sets","volume":"63","author":"Dushnik","year":"1941","journal-title":"Am. J. Math."},{"issue":"3","key":"10.1016\/j.jcta.2026.106215_br0080","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/rsa.3240020302","article-title":"The dimension of random ordered sets","volume":"2","author":"Erd\u0151s","year":"1991","journal-title":"Random Struct. Algorithms"},{"key":"10.1016\/j.jcta.2026.106215_br0090","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1090\/S0002-9904-1947-08785-1","article-title":"Some remarks on the theory of graphs","volume":"53","author":"Erd\u00f6s","year":"1947","journal-title":"Bull. Am. Math. Soc."},{"key":"10.1016\/j.jcta.2026.106215_br0100","first-page":"463","article-title":"A combinatorial problem in geometry","volume":"2","author":"Erd\u0151s","year":"1935","journal-title":"Compos. Math."},{"issue":"5","key":"10.1016\/j.jcta.2026.106215_br0110","doi-asserted-by":"crossref","DOI":"10.1007\/s00373-024-02825-1","article-title":"New tools to study 1-11-representation of graphs","volume":"40","author":"Futorny","year":"2024","journal-title":"Graphs Comb."},{"key":"10.1016\/j.jcta.2026.106215_br0120","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.dam.2018.03.013","article-title":"On the representation number of a crown graph","volume":"244","author":"Glen","year":"2018","journal-title":"Discrete Appl. Math."},{"issue":"2","key":"10.1016\/j.jcta.2026.106215_br0130","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1017\/S0013091525101211","article-title":"k-11-representations of graphs, revisited","volume":"69","author":"Hefty","year":"2026","journal-title":"Proc. Edinb. Math. Soc. (2)"},{"issue":"4","key":"10.1016\/j.jcta.2026.106215_br0140","article-title":"Word-representable graphs: orientations, posets, and bounds","volume":"31","author":"Hefty","year":"2024","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.jcta.2026.106215_br0150","series-title":"Graph-Theoretic Concepts in Computer Science","first-page":"191","article-title":"Alternation graphs","volume":"vol. 6986","author":"Halld\u00f3rsson","year":"2011"},{"key":"10.1016\/j.jcta.2026.106215_br0160","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.dam.2015.07.033","article-title":"Semi-transitive orientations and word-representable graphs","volume":"201","author":"Halld\u00f3rsson","year":"2016","journal-title":"Discrete Appl. Math."},{"key":"10.1016\/j.jcta.2026.106215_br0170","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0012-365X(81)90203-X","article-title":"On the dimension of partially ordered sets","volume":"35","author":"Kelly","year":"1981","journal-title":"Discrete Math."},{"issue":"1\u20133","key":"10.1016\/j.jcta.2026.106215_br0180","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/S0012-365X(98)00316-1","article-title":"The dimension of two levels of the Boolean lattice","volume":"201","author":"Kierstead","year":"1999","journal-title":"Discrete Math."},{"key":"10.1016\/j.jcta.2026.106215_br0190","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-25859-1","article-title":"Words and Graphs","author":"Kitaev","year":"2015"},{"key":"10.1016\/j.jcta.2026.106215_br0200","series-title":"Developments in Language Theory","first-page":"156","article-title":"On word-representable and multi-word-representable graphs","volume":"vol. 13911","author":"Kenkireth","year":"2023"},{"issue":"1","key":"10.1016\/j.jcta.2026.106215_br0210","first-page":"45","article-title":"On representable graphs","volume":"13","author":"Kitaev","year":"2008","journal-title":"J. Autom. Lang. Comb."},{"key":"10.1016\/j.jcta.2026.106215_br0220","author":"Mozhui"},{"issue":"1","key":"10.1016\/j.jcta.2026.106215_br0230","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s00493-011-2630-7","article-title":"The structure of hereditary properties and 2-coloured multigraphs","volume":"31","author":"Marchant","year":"2011","journal-title":"Combinatorica"},{"key":"10.1016\/j.jcta.2026.106215_br0240","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF01896428","article-title":"Minimal scrambling sets of simple orders","volume":"22","author":"Spencer","year":"1971","journal-title":"Acta Math. Acad. Sci. Hung."}],"container-title":["Journal of Combinatorial Theory, Series A"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0097316526000580?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0097316526000580?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T16:46:25Z","timestamp":1780677985000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0097316526000580"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":24,"alternative-id":["S0097316526000580"],"URL":"https:\/\/doi.org\/10.1016\/j.jcta.2026.106215","relation":{},"ISSN":["0097-3165"],"issn-type":[{"value":"0097-3165","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Word-representation numbers of graphs: Bottlenecks and bounds","name":"articletitle","label":"Article Title"},{"value":"Journal of Combinatorial Theory, Series A","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcta.2026.106215","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"106215"}}