{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T09:44:39Z","timestamp":1698227079280},"reference-count":3,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4480,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1994,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic><jats:bold>K<\/jats:bold><\/jats:italic> be a cardinal. If <jats:italic><jats:bold>K<\/jats:bold><\/jats:italic> \u03c7<jats:sub>0<\/jats:sub>, define <jats:bold>K<\/jats:bold>:= <jats:italic><jats:bold>K<\/jats:bold><\/jats:italic>. Otherwise, let <jats:italic><jats:bold>K<\/jats:bold><\/jats:italic> := <jats:italic><jats:bold>K<\/jats:bold><\/jats:italic> + 1. We prove a conjecture of Mader: Every infinite <jats:italic><jats:bold>K<\/jats:bold><\/jats:italic>\u2010connected graph <jats:italic>G<\/jats:italic> = (<jats:italic>V, E<\/jats:italic>) contains a set <jats:italic>S<\/jats:italic> \u2286 <jats:italic>V<\/jats:italic> with |<jats:italic>S<\/jats:italic>| = |<jats:italic>V<\/jats:italic>| such that <jats:italic>G\/S<\/jats:italic> is <jats:italic><jats:bold>K<\/jats:bold><\/jats:italic>\u2010connected for all <jats:italic>S<\/jats:italic>\u2286 <jats:italic>S<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/jgt.3190180411","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:18:30Z","timestamp":1181240310000},"page":"413-426","source":"Crossref","is-referenced-by-count":1,"title":["Large <i>k<\/i>\u2010preserving sets in infinite graphs"],"prefix":"10.1002","volume":"18","author":[{"given":"Andreas","family":"Huck","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Niedermeyer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Set Theory","author":"Jech T.","year":"1978"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-0517-7_13"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511983917.036"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190180411","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190180411","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T16:21:58Z","timestamp":1698164518000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190180411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,7]]},"references-count":3,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,7]]}},"alternative-id":["10.1002\/jgt.3190180411"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190180411","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,7]]}}}