{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T23:04:32Z","timestamp":1744412672519,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,2,15]],"date-time":"2020-02-15T00:00:00Z","timestamp":1581724800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,2,15]],"date-time":"2020-02-15T00:00:00Z","timestamp":1581724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY20A010013"],"award-info":[{"award-number":["LY20A010013"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11401389"],"award-info":[{"award-number":["11401389"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201608330111"],"award-info":[{"award-number":["201608330111"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11971349"],"award-info":[{"award-number":["11971349"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871280","11971349"],"award-info":[{"award-number":["11871280","11971349"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11531011","11771013"],"award-info":[{"award-number":["11531011","11771013"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61751303"],"award-info":[{"award-number":["61751303"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LD19A010001","LY19A010018"],"award-info":[{"award-number":["LD19A010001","LY19A010018"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013088","name":"Qinglan Project of Jiangsu Province of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013088","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10878-020-00541-z","type":"journal-article","created":{"date-parts":[[2020,2,15]],"date-time":"2020-02-15T16:02:26Z","timestamp":1581782546000},"page":"1741-1752","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Computation and algorithm for the minimum k-edge-connectivity of graphs"],"prefix":"10.1007","volume":"44","author":[{"given":"Yuefang","family":"Sun","sequence":"first","affiliation":[]},{"given":"Chenchen","family":"Wu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3085-2701","authenticated-orcid":false,"given":"Xiaoyan","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Zhao","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,15]]},"reference":[{"key":"541_CR1","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1137\/0134052","volume":"34","author":"FT Boesch","year":"1978","unstructured":"Boesch FT, Chen S (1978) A generalization of line connectivity and optimally invulnerable graphs. SIAM J Appl Math 34:657\u2013665","journal-title":"SIAM J Appl Math"},{"key":"541_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph theory, GTM 244","author":"JA Bondy","year":"2008","unstructured":"Bondy JA, Murty USR (2008) Graph theory, GTM 244. Springer, Berlin"},{"issue":"5","key":"541_CR3","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/S0167-6377(97)00043-6","volume":"21","author":"M Burlet","year":"1997","unstructured":"Burlet M, Goldschmidt O (1997) A new and improved algorithm for the 3-cut problem. Oper Res Lett 21(5):225\u2013227","journal-title":"Oper Res Lett"},{"issue":"10","key":"541_CR4","doi-asserted-by":"publisher","first-page":"2668","DOI":"10.1109\/TAC.2014.2328757","volume":"59","author":"A Chapman","year":"2014","unstructured":"Chapman A, Nabi-Abdolyousefi M, Mesbahi M (2014) Controllability and observability of networks-of-networks via Cartesian Products. IEEE Trans Automat Control 59(10):2668\u20132679","journal-title":"IEEE Trans Automat Control"},{"key":"541_CR5","first-page":"1","volume":"2","author":"G Chartrand","year":"1984","unstructured":"Chartrand G, Kappor SF, Lesniak L, Lick DR (1984) Generalized connectivity in graphs. Bull Bombay Math Colloq 2:1\u20136","journal-title":"Bull Bombay Math Colloq"},{"issue":"1","key":"541_CR6","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10878-015-9955-x","volume":"33","author":"L Chen","year":"2017","unstructured":"Chen L, Li X, Liu M, Mao Y (2017) A solution to a conjecture on the generalized connectivity of graphs. J Comb Optim 33(1):275\u2013282","journal-title":"J Comb Optim"},{"key":"541_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-21275-3","volume-title":"Parameterized algorithms","author":"M Cygan","year":"2015","unstructured":"Cygan M, Fomin FV, Kowalik L, Lokshtanov D, Marx D, Pilipczuk M, Pilipczuk M, Saurabh S (2015) Parameterized algorithms. Springer, Berlin"},{"key":"541_CR8","doi-asserted-by":"crossref","unstructured":"Cygan M, Kratsch S, Pilipczuk M, Pilipczuk M, Wahlstr\u00f6m M (2014) Clique cover and graph separation: new Incompressibility results, ACM Trans Comput Theory 6(2), Article 6","DOI":"10.1145\/2594439"},{"key":"541_CR9","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/S1571-0661(04)81014-4","volume":"78","author":"RG Downey","year":"2003","unstructured":"Downey RG, Estivill-Castro V, Fellows MR, Prieto E, Rosamond FA (2003) Cutting up is hard to do: the parameterized complexity of $$k$$-cut and related problems. Electr Notes Theor Comput Sci 78:209\u2013222","journal-title":"Electr Notes Theor Comput Sci"},{"issue":"1","key":"541_CR10","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1287\/moor.19.1.24","volume":"19","author":"O Goldschmidt","year":"1994","unstructured":"Goldschmidt O, Hochbaum DS (1994) A polynomial algorithm for the $$k$$-cut problem for fixed $$k$$. Math Oper Res 19(1):24\u201337","journal-title":"Math Oper Res"},{"key":"541_CR11","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0095-8956(85)90083-8","volume":"38","author":"M Hager","year":"1985","unstructured":"Hager M (1985) Pendant tree-connectivity. J Combin Theory Ser B 38:179\u2013189","journal-title":"J Combin Theory Ser B"},{"key":"541_CR12","series-title":"Lecture notes in math. 303","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BFb0067365","volume-title":"Graph theory and applications","author":"ST Hedetniemi","year":"1972","unstructured":"Hedetniemi ST, Slater PJ (1972) Line graphs of triangleless graphs and iterated clique graphs. In: Alavi Y et al (eds) Graph theory and applications. Lecture notes in math. 303. Springer, Berlin, pp 139\u2013147"},{"key":"541_CR13","first-page":"271","volume-title":"Selected topics in graph theory","author":"R Hemminger","year":"1978","unstructured":"Hemminger R, Beineke L (1978) Line graphs and line digraphs. In: Beineke L et al (eds) Selected topics in graph theory. Academic Press, London, pp 271\u2013305"},{"key":"541_CR14","volume-title":"Product graphs-structure and recognition","author":"W Imrich","year":"2000","unstructured":"Imrich W, Klav\u017ear S (2000) Product graphs-structure and recognition. Wiley, New York"},{"issue":"5","key":"541_CR15","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1137\/050631616","volume":"36","author":"Y Kamidoi","year":"2007","unstructured":"Kamidoi Y, Yoshida N, Nagamochi H (2007) A deterministic algorithm for finding all minimum $$k$$-way cuts. SIAM J Comput 36(5):1329\u20131341","journal-title":"SIAM J Comput"},{"key":"541_CR16","doi-asserted-by":"crossref","unstructured":"Kawarabayashi K, Thorup M (2011) The minimum $$k$$-way cut of bounded size is fixed parameter tractable, In: Proceedings of FOCS. pp 160\u2013169","DOI":"10.1109\/FOCS.2011.53"},{"key":"541_CR17","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.disc.2009.07.026","volume":"310","author":"M Knor","year":"2010","unstructured":"Knor M, Zhou S (2010) Diameter and connectivity of 3-arc graphs. Discret Math 310:37\u201342","journal-title":"Discret Math"},{"issue":"1","key":"541_CR18","first-page":"43","volume":"14","author":"H Li","year":"2012","unstructured":"Li H, Li X, Sun Y (2012) The generalized 3-connectivity of Cartesian product graphs. Discret Math Theor Comput Sci 14(1):43\u201354","journal-title":"Discret Math Theor Comput Sci"},{"issue":"1","key":"541_CR19","first-page":"339","volume":"16","author":"X Li","year":"2014","unstructured":"Li X, Mao Y (2014) The generalized 3-connectivity of lexicographic product graphs. Discret Math Theor Comput Sci 16(1):339\u2013354","journal-title":"Discret Math Theor Comput Sci"},{"key":"541_CR20","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.dam.2014.12.009","volume":"185","author":"X Li","year":"2015","unstructured":"Li X, Mao Y (2015) Nordhaus-Gaddum-type results for the generalized edge-connectivity of graphs. Discret Appl Math 185:102\u2013112","journal-title":"Discret Appl Math"},{"key":"541_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-33828-6","volume-title":"Generalized connectivity of graphs, Springe briefs in mathematics","author":"X Li","year":"2016","unstructured":"Li X, Mao Y (2016) Generalized connectivity of graphs, Springe briefs in mathematics. Springer, Switzerland"},{"key":"541_CR22","first-page":"304","volume":"58","author":"X Li","year":"2014","unstructured":"Li X, Mao Y, Sun Y (2014) On the generalized (edge-)connectivity of graphs. Australas J Combin 58:304\u2013319","journal-title":"Australas J Combin"},{"key":"541_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00373-012-1243-2","volume":"29","author":"X Li","year":"2013","unstructured":"Li X, Shi Y, Sun Y (2013) Rainbow connections of graphs: a survey. Graphs Combin 29:1\u201338","journal-title":"Graphs Combin"},{"key":"541_CR24","doi-asserted-by":"crossref","unstructured":"Li X, Yue J, Zhao Y (2014) The generalized 3-edge-connectivity of lexicographic product graphs, In: Proceedings of COCOA 2014, LNCS 8881, pp 412\u2013425","DOI":"10.1007\/978-3-319-12691-3_31"},{"key":"541_CR25","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/BF01788551","volume":"3","author":"OR Oellermann","year":"1987","unstructured":"Oellermann OR (1987) On the $$\\ell $$-connectivity of a graph. Graphs Combin 3:285\u2013299","journal-title":"Graphs Combin"},{"issue":"1","key":"541_CR26","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s10587-015-0162-9","volume":"65","author":"Y Sun","year":"2015","unstructured":"Sun Y (2015) Generalized 3-edge-connectivity of Cartesian product graphs. Czechoslovak Math J 65(1):107\u2013117","journal-title":"Czechoslovak Math J"},{"issue":"3","key":"541_CR27","doi-asserted-by":"publisher","first-page":"623","DOI":"10.7151\/dmgt.1941","volume":"37","author":"Y Sun","year":"2017","unstructured":"Sun Y (2017a) On the maximum and minimum sizes of a graph with given $$k$$-connectivity. Discuss Math Graph Theory 37(3):623\u2013632","journal-title":"Discuss Math Graph Theory"},{"issue":"4","key":"541_CR28","doi-asserted-by":"publisher","first-page":"975","DOI":"10.7151\/dmgt.1982","volume":"37","author":"Y Sun","year":"2017","unstructured":"Sun Y (2017b) A sharp lower bound for the generalized 3-edge-connectivity of strong product graphs. Discuss Math Graph Theory 37(4):975\u2013988","journal-title":"Discuss Math Graph Theory"},{"issue":"1","key":"541_CR29","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s10878-015-9956-9","volume":"33","author":"Y Sun","year":"2017","unstructured":"Sun Y, Li X (2017) On the difference of two generalized connectivities of a graph. J Comb Optim 33(1):283\u2013291","journal-title":"J Comb Optim"},{"issue":"4","key":"541_CR30","doi-asserted-by":"publisher","first-page":"1673","DOI":"10.1007\/s40840-015-0147-8","volume":"39","author":"Y Sun","year":"2016","unstructured":"Sun Y, Zhou S (2016) Tree connectivities of Cayley graphs on Abelian groups with small degrees. Bull Malays Math Sci Soc 39(4):1673\u20131685","journal-title":"Bull Malays Math Sci Soc"},{"key":"541_CR31","doi-asserted-by":"crossref","unstructured":"Thorup M (2008) Minimum $$k$$-way cuts via deterministic greedy tree packing, In: Proceedings of STOC. ACM. pp 159\u2013166","DOI":"10.1145\/1374376.1374402"},{"key":"541_CR32","volume-title":"Introduction to graph theory","author":"DB West","year":"2001","unstructured":"West DB (2001) Introduction to graph theory, 2nd edn. Prentice Hall, Upper Saddle River","edition":"2"},{"key":"541_CR33","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.disc.2005.11.010","volume":"306","author":"J Xu","year":"2006","unstructured":"Xu J, Yang C (2006) Connectivity of Cartesian product graphs. Discret Math 306:159\u2013165","journal-title":"Discret Math"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-020-00541-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-020-00541-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-020-00541-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T08:45:19Z","timestamp":1664354719000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-020-00541-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,15]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["541"],"URL":"https:\/\/doi.org\/10.1007\/s10878-020-00541-z","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"type":"print","value":"1382-6905"},{"type":"electronic","value":"1573-2886"}],"subject":[],"published":{"date-parts":[[2020,2,15]]},"assertion":[{"value":"15 February 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}