{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T14:05:40Z","timestamp":1772373940489,"version":"3.50.1"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:p>An infinite graph \u0393 is minor excluded if there is a finite graph that is not a minor of \u0393. We prove that minor excluded graphs have finite Assouad\u2013Nagata dimension and study minor exclusion for Cayley graphs of finitely generated groups. Our main results and observations are: (1) minor exclusion is not a group property: it depends on the choice of generating set; (2) a group with one end has a generating set for which the Cayley graph is not minor excluded; (3) there are groups that are not minor excluded for any set of generators, like \u2124<jats:sup>3<\/jats:sup>; (4) minor exclusion is preserved under free products; and (5) virtually free groups are minor excluded for any choice of finite generating set.<\/jats:p>","DOI":"10.1142\/s0218196715500095","type":"journal-article","created":{"date-parts":[[2015,2,25]],"date-time":"2015-02-25T10:11:16Z","timestamp":1424859076000},"page":"541-554","source":"Crossref","is-referenced-by-count":10,"title":["Metric dimensions of minor excluded graphs and minor exclusion in groups"],"prefix":"10.1142","volume":"25","author":[{"given":"Mikhail I.","family":"Ostrovskii","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Queens, NY 11439, USA"}]},{"given":"David","family":"Rosenthal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Queens, NY 11439, USA"}]}],"member":"219","published-online":{"date-parts":[[2015,5,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(87)90006-2"},{"key":"rf2","doi-asserted-by":"crossref","first-page":"589","DOI":"10.36045\/bbms\/1102689123","volume":"11","author":"Arzhantseva G. N.","year":"2004","journal-title":"Bull. Belg. Math. Soc. Simon Stevin"},{"key":"rf3","first-page":"31","volume":"294","author":"Assouad P.","year":"1982","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010207"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12494-9"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.4171\/036"},{"key":"rf7","series-title":"Chicago Lectures in Mathematics","volume-title":"Topics in Geometric Group Theory","author":"de la Harpe P.","year":"2000"},{"key":"rf8","series-title":"Graduate Texts in Mathematics","volume-title":"Graph Theory","volume":"173","author":"Diestel R.","year":"2000"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-013-0234-7"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(54)50043-0"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1515\/JGT.2006.032"},{"key":"rf12","first-page":"269","volume":"39","author":"Droms C.","year":"1998","journal-title":"Beitr\u00e4ge Algebra Geom."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45198-3_4"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2013.07.014"},{"key":"rf15","unstructured":"M.\u00a0Gromov, Geometric Group Theory, London Mathematical Society Lecture Notes Series\u00a0182, eds. A.\u00a0Niblo and M.\u00a0Roller (Cambridge University Press, 1993)\u00a0pp. 1\u2013295."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02993589"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1155\/IMRN.2005.3625"},{"key":"rf19","first-page":"207","volume":"36","author":"Levinson H.","year":"1982","journal-title":"Congr. Numer."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139167505"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1112\/S0010437X11005343"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.4171\/112"},{"key":"rf23","first-page":"415","volume":"62","author":"Ostrovskii M. I.","year":"2009","journal-title":"C. R. Acad. Bulgare Sci."},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1515\/9783110264012"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1007\/s10711-005-0548-1"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8594-1"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306007838"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089692"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196715500095","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,30]],"date-time":"2020-08-30T08:30:41Z","timestamp":1598776241000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196715500095"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,21]]},"references-count":27,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2015,5,21]]},"published-print":{"date-parts":[[2015,6]]}},"alternative-id":["10.1142\/S0218196715500095"],"URL":"https:\/\/doi.org\/10.1142\/s0218196715500095","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,21]]}}}