{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T21:28:22Z","timestamp":1698355702582},"reference-count":7,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5056,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider finite undirected loopless graphs <jats:italic>G<\/jats:italic> in which multiple edges are possible. For integers k,l \u2265 0 let g(k, l) be the minimal <jats:italic>n<\/jats:italic> \u2265 0 with the following property: If <jats:italic>G<\/jats:italic> is an <jats:italic>n<\/jats:italic>\u2010edge\u2010connected graph, <jats:italic>s<\/jats:italic><jats:sub>1<\/jats:sub>, \u20db,<jats:italic>s<\/jats:italic><jats:sub>k<\/jats:sub>, <jats:italic>t<\/jats:italic><jats:sub>1<\/jats:sub>, \u20db,<jats:italic>t<\/jats:italic><jats:sub>k<\/jats:sub> are vertices of <jats:italic>G<\/jats:italic>, and <jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>, \u20db,<jats:italic>f<\/jats:italic><jats:sub>l<\/jats:sub>, <jats:italic>g<\/jats:italic><jats:sub>1<\/jats:sub>, \u20db,<jats:italic>g<\/jats:italic><jats:sub>l<\/jats:sub>, are pairwise distinct edges of <jats:italic>G<\/jats:italic>, then for each <jats:italic>i<\/jats:italic> = 1, \u20db, <jats:italic>k<\/jats:italic> there exists a path <jats:italic>P<\/jats:italic><jats:sub>i<\/jats:sub> in <jats:italic>G<\/jats:italic>, connecting <jats:italic>s<\/jats:italic><jats:sub>i<\/jats:sub> and <jats:italic>t<\/jats:italic><jats:sub>i<\/jats:sub> and for each <jats:italic>i<\/jats:italic> = 1, \u20db,<jats:italic>l<\/jats:italic> there exists a cycle <jats:italic>C<\/jats:italic><jats:sub>i<\/jats:sub> in <jats:italic>G<\/jats:italic> containing <jats:italic>f<\/jats:italic><jats:sub>i<\/jats:sub> and <jats:italic>g<\/jats:italic><jats:sub>i<\/jats:sub> such that <jats:italic>P<\/jats:italic><jats:sub>1<\/jats:sub>, \u20db,<jats:italic>P<\/jats:italic><jats:sub>k<\/jats:sub>, <jats:italic>C<\/jats:italic><jats:sub>1<\/jats:sub>, \u20db, <jats:italic>C<\/jats:italic><jats:sub>l<\/jats:sub> are pairwise edge\u2010disjoint. We give upper and lower bounds for <jats:italic>g<\/jats:italic>(<jats:italic>k, l<\/jats:italic>).<\/jats:p>","DOI":"10.1002\/jgt.3190160605","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T22:31:50Z","timestamp":1181255510000},"page":"571-589","source":"Crossref","is-referenced-by-count":1,"title":["Edge\u2010disjoint paths and cycles in <i>n<\/i>\u2010edge\u2010connected graphs"],"prefix":"10.1002","volume":"16","author":[{"given":"Andreas","family":"Huck","sequence":"first","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":"10.1016\/0095-8956(84)90015-7"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01787639"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70504-1"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","first-page":"99","DOI":"10.4099\/math1924.10.99","article-title":"Multicommodity flows in graphs II","volume":"10","author":"Okamura H.","year":"1984","journal-title":"Jpn. 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