{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T16:16:52Z","timestamp":1772468212536,"version":"3.50.1"},"reference-count":8,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4844,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>From a theorem of W. Mader [\u201c\u00dcber minimal <jats:italic>n<\/jats:italic>\u2010fach zusammenh\u00e4ngende unendliche Graphen und ein Extremal problem,\u201d <jats:italic>Arch. Mat.<\/jats:italic>, Vol. 23 (1972), pp. 553\u2013560] it follows that a <jats:italic>k<\/jats:italic>\u2010connected (<jats:italic>k<\/jats:italic>\u2010edge\u2010connected) graph <jats:italic>G<\/jats:italic> = (<jats:italic>V,E<\/jats:italic>) always contains a <jats:italic>k<\/jats:italic>\u2010connected (<jats:italic>k<\/jats:italic>\u2010edge\u2010connected) subgraph <jats:italic>G\u2032<\/jats:italic> = (<jats:italic>V,E\u2032<\/jats:italic>) with <jats:italic>O<\/jats:italic>(<jats:italic>k<\/jats:italic>|<jats:italic>V<\/jats:italic>|) edges. T. Nishizeki and S. Poljak \u201c<jats:italic>K<\/jats:italic>\u2010Connectivity and Decomposition of Graphs into Forests,\u201d Discrete Applied Mathematics, submitted) showed how <jats:italic>G\u2032<\/jats:italic> can be constructed as the union of <jats:italic>k<\/jats:italic> forests. H. Nagamochi and T. Ibaraki [A Linear Time Algorithm for Finding a Sparse <jats:italic>k<\/jats:italic>\u2010Connected Spanning Subgraph of a <jats:italic>k<\/jats:italic>\u2010Connected Graph, <jats:italic>Algorithmica<\/jats:italic>, Vol. 7 (1992), pp. 583\u2013596] constructed such a subgraph <jats:italic>G<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> in linear time and showed for any pair <jats:italic>x,y<\/jats:italic> of nodes that <jats:italic>G<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> contains <jats:italic>k<\/jats:italic> openly disjoint (edge\u2010disjoint) paths connecting <jats:italic>x<\/jats:italic> and <jats:italic>y<\/jats:italic> if <jats:italic>G<\/jats:italic> contains <jats:italic>k<\/jats:italic> openly disjoint (edge\u2010disjoint) paths connecting <jats:italic>x<\/jats:italic> and <jats:italic>y<\/jats:italic> (even if <jats:italic>G<\/jats:italic> is not <jats:italic>k<\/jats:italic>\u2010connected (<jats:italic>k<\/jats:italic>\u2010edge\u2010connected)). In this article we provide a much shorter proof of a common generalization of the edge\u2010 and node\u2010connectivity versions showing that the subgraph <jats:italic>G<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> has a certain mixed connectivity property. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170302","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:22:26Z","timestamp":1181240546000},"page":"275-281","source":"Crossref","is-referenced-by-count":35,"title":["On sparse subgraphs preserving connectivity properties"],"prefix":"10.1002","volume":"17","author":[{"given":"Andr\u00e1s","family":"Frank","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toshihide","family":"Ibaraki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroshi","family":"Nagamochi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400875184"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01304933"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01432512"},{"key":"e_1_2_1_5_2","first-page":"293","article-title":"Connectivity and edge\u2010connectivity in finite graphs","volume":"38","author":"Mader W.","year":"1979","journal-title":"Surveys on Combinatorics"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01758778"},{"key":"e_1_2_1_8_2","unstructured":"T.NishizekiandS.Poljak K\u2010connectivity and decomposition of graphs into forests.Discrete Appl. Math.Submitted."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/0213035"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190170302","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170302","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T12:09:19Z","timestamp":1698235759000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,7]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,7]]}},"alternative-id":["10.1002\/jgt.3190170302"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170302","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,7]]}}}