{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T03:09:23Z","timestamp":1761620963060},"reference-count":18,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7611,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1985,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For any positive integer <jats:italic>s<\/jats:italic>, an <jats:italic>s<\/jats:italic>\u2010partition of a graph <jats:italic>G<\/jats:italic> = (<jats:italic>V<\/jats:italic>, <jats:italic>E<\/jats:italic>) is a partition of <jats:italic>E<\/jats:italic> into <jats:italic>E<\/jats:italic><jats:sub>1<\/jats:sub> \u222a <jats:italic>E<\/jats:italic><jats:sub>2<\/jats:sub> \u222a\u2026\ufe01 \u222a <jats:italic>E<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>, where \u2223<jats:italic>E<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>\u2223 = <jats:italic>s<\/jats:italic> for 1 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>k<\/jats:italic> \u2212 1 and 1 \u2264 \u2223<jats:italic>E<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>\u2223 \u2264 <jats:italic>s<\/jats:italic> and each <jats:italic>E<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> induces a connected subgraph of <jats:italic>G.<\/jats:italic> We prove\n<jats:list list-type=\"explicit-label\">\n<jats:list-item><jats:p>If <jats:italic>G<\/jats:italic> is connected, then there exists a 2\u2010partition, but not necessarily a 3\u2010partition;<\/jats:p><\/jats:list-item>\n<jats:list-item><jats:p>If <jats:italic>G<\/jats:italic> is 2\u2010edge connected, then there exists a 3\u2010partition, but not necessarily a 4\u2010partition;<\/jats:p><\/jats:list-item>\n<jats:list-item><jats:p>If <jats:italic>G<\/jats:italic> is 3\u2010edge connected, then there exists a 4\u2010partition;<\/jats:p><\/jats:list-item>\n<jats:list-item><jats:p>If <jats:italic>G<\/jats:italic> is 4\u2010edge connected, then there exists an <jats:italic>s<\/jats:italic>\u2010partition for all <jats:italic>s<\/jats:italic>.<\/jats:p><\/jats:list-item>\n<\/jats:list><\/jats:p>","DOI":"10.1002\/jgt.3190090416","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T11:47:55Z","timestamp":1180180075000},"page":"539-549","source":"Crossref","is-referenced-by-count":43,"title":["On partitioning the edges of graphs into connected subgraphs"],"prefix":"10.1002","volume":"9","author":[{"given":"M.","family":"J\u00fcnger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Reinelt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"W. 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