{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:16:43Z","timestamp":1740104203066,"version":"3.37.3"},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2017,9,18]],"date-time":"2017-09-18T00:00:00Z","timestamp":1505692800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SCHM 3186\/1\u20101"],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2018,5]]},"abstract":"Abstract<\/jats:title>For minimally k<\/jats:italic>\u2010connected graphs on n<\/jats:italic> vertices, Mader proved a tight lower bound for the number of vertices of degree k<\/jats:italic> in dependence on n<\/jats:italic> and k<\/jats:italic>. Oxley observed 1981 that in many cases a considerably better bound can be given if is used as additional parameter, i.e. in dependence on m<\/jats:italic>, n<\/jats:italic>, and k<\/jats:italic>. It was left open to determine whether Oxley's more general bound is best possible. We show that this is not the case, but give a closely related bound that deviates from a variant of Oxley's long\u2010standing one only for small values of m<\/jats:italic>. We prove that this new bound is best possible. The bound contains Mader's bound as special case.<\/jats:p>","DOI":"10.1002\/jgt.22202","type":"journal-article","created":{"date-parts":[[2017,9,18]],"date-time":"2017-09-18T14:59:29Z","timestamp":1505746769000},"page":"146-153","source":"Crossref","is-referenced-by-count":2,"title":["Tight bounds for the vertices of degree k in minimally k\u2010connected graphs"],"prefix":"10.1002","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3032-4834","authenticated-orcid":false,"given":"Jens M.","family":"Schmidt","sequence":"first","affiliation":[{"name":"Institute of Mathematics TU Ilmenau Ilmenau Germany"}]}],"member":"311","published-online":{"date-parts":[[2017,9,18]]},"reference":[{"volume-title":"Extremal graph theory","year":"2004","author":"Bollob\u00e1s B.","key":"e_1_2_5_2_1"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1967.228.204"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1201\/b16132"},{"key":"e_1_2_5_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(69)80049-9"},{"key":"e_1_2_5_6_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.48.7.1142"},{"key":"e_1_2_5_7_1","first-page":"71","volume-title":"Topics in structural graph theory","author":"Kriesell M.","year":"2013"},{"key":"e_1_2_5_8_1","first-page":"201","article-title":"Minimale n\u2010fach zusammenh\u00e4ngende Graphen mit maximaler Kantenzahl","volume":"249","author":"Mader W.","year":"1971","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"e_1_2_5_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01304873"},{"key":"e_1_2_5_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02950646"},{"key":"e_1_2_5_11_1","first-page":"423","article-title":"On vertices of degree n in minimally n\u2010connected graphs and digraphs","volume":"2","author":"Mader W.","year":"1996","journal-title":"Bolyai Soc. 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