{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T14:17:12Z","timestamp":1768745832759,"version":"3.49.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:00:00Z","timestamp":1559865600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:00:00Z","timestamp":1559865600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11531011"],"award-info":[{"award-number":["11531011"]}],"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":["11771039"],"award-info":[{"award-number":["11771039"]}],"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":["11771443"],"award-info":[{"award-number":["11771443"]}],"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":["11861066"],"award-info":[{"award-number":["11861066"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s00373-019-02052-z","type":"journal-article","created":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T13:02:40Z","timestamp":1559912560000},"page":"1001-1010","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On the Sizes of Vertex-k-Maximal r-Uniform Hypergraphs"],"prefix":"10.1007","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1595-9834","authenticated-orcid":false,"given":"Yingzhi","family":"Tian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong-Jian","family":"Lai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jixiang","family":"Meng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,6,7]]},"reference":[{"key":"2052_CR1","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1002\/jgt.22008","volume":"84","author":"J Anderson","year":"2017","unstructured":"Anderson, J., Lai, H.-J., Lin, X., Xu, M.: On $$k$$-maximal strength digraphs. J. Graph Theory 84, 17\u201325 (2017)","journal-title":"J. Graph Theory"},{"issue":"2","key":"2052_CR2","first-page":"0","volume":"2","author":"MA Bahmanian","year":"2015","unstructured":"Bahmanian, M.A., S\u0306ajna, M.: Connection and separation in hypergraphs. Theory Appl. Graphs 2(2), 0\u201324 (2015)","journal-title":"Theory Appl. Graphs"},{"key":"2052_CR3","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1016\/j.disc.2015.10.014","volume":"339","author":"A Bernshteyn","year":"2016","unstructured":"Bernshteyn, A., Kostochka, A.: On the number of edges in a graph with no ($$k+1$$)-connected subgraphs. Discrete Math. 339, 682\u2013688 (2016)","journal-title":"Discrete Math."},{"key":"2052_CR4","volume-title":"Graph Theory, Graduate Texts in Mathematics","author":"JA Bondy","year":"2008","unstructured":"Bondy, J.A., Murty, U.S.R.: Graph Theory, Graduate Texts in Mathematics. Springer, Berlin (2008)"},{"key":"2052_CR5","unstructured":"Chekuri C., Xu C.: Computing minimum cuts in hypergraphs. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (Barcelona, 2017), pp. 1085\u20131100. SIAM (2017)"},{"issue":"2","key":"2052_CR6","doi-asserted-by":"publisher","first-page":"252","DOI":"10.4153\/CMB-2018-005-9","volume":"61","author":"M Dewar","year":"2016","unstructured":"Dewar, M., Pike, D., Proos, J.: Connectivity in Hypergraphs. Can. Math. Bull. 61(2), 252\u2013271 (2016)","journal-title":"Can. Math. Bull."},{"key":"2052_CR7","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1002\/jgt.3190140207","volume":"14","author":"H-J Lai","year":"1990","unstructured":"Lai, H.-J.: The size of strength-maximal graphs. J. Graph Theory 14, 187\u2013197 (1990)","journal-title":"J. Graph Theory"},{"key":"2052_CR8","doi-asserted-by":"publisher","first-page":"2500","DOI":"10.1016\/j.disc.2016.04.007","volume":"339","author":"X Lin","year":"2016","unstructured":"Lin, X., Fan, S., Lai, H.-J., Xu, M.: On the lower bound of $$k$$-maximal digraphs. Discrete Math. 339, 2500\u20132510 (2016)","journal-title":"Discrete Math."},{"key":"2052_CR9","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/BF01433466","volume":"191","author":"W Mader","year":"1971","unstructured":"Mader, W.: Minimale $$n$$-fach kantenzusammenhngende graphen. Math. Ann. 191, 21\u201328 (1971)","journal-title":"Math. Ann."},{"key":"2052_CR10","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1007\/BF02993903","volume":"37","author":"W Mader","year":"1972","unstructured":"Mader, W.: Existenz $$n$$-fach zusammenh$$\\ddot{a}$$ngender Teilgraphen in Graphen gen$$\\ddot{u}$$gend gro$$\\beta $$en Kantendichte. Abh. Math. Sem. Univ. Hambg. 37, 86\u201397 (1972)","journal-title":"Abh. Math. Sem. Univ. Hambg."},{"key":"2052_CR11","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1017\/CBO9780511662133.005","volume-title":"Surveys in Combinatorics","author":"W Mader","year":"1979","unstructured":"Mader, W.: Connectivity and edge-connectivity in finite graphs. In: Bollob\u00e1s, B. (ed.) Surveys in Combinatorics, pp. 66\u201395. Cambridge University Press, London (1979)"},{"key":"2052_CR12","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/BFb0060120","volume-title":"The Many Facets of Graph Theory. Lecture Notes in Mathematics, No. 110","author":"DW Matula","year":"1969","unstructured":"Matula, D.W.: The cohesive strength of graphs. In: Chartrand, G., Kapoor, S.F. (eds.) The Many Facets of Graph Theory. Lecture Notes in Mathematics, No. 110, pp. 215\u2013221. Springer, Berlin (1969)"},{"key":"2052_CR13","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1137\/0122040","volume":"22","author":"DW Matula","year":"1972","unstructured":"Matula, D.W.: $$K$$-components, clusters, and slicings in graphs. SIAM J. Appl. Math. 22, 459\u2013480 (1972)","journal-title":"SIAM J. Appl. Math."},{"key":"2052_CR14","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/BFb0070394","volume-title":"Subgraph Connectivity Numbers of a Graph. Theory and Applications of Graphs","author":"DW Matula","year":"1978","unstructured":"Matula, D.W.: Subgraph Connectivity Numbers of a Graph. Theory and Applications of Graphs, pp. 371\u2013383. Springer, Berlin (1978)"},{"key":"2052_CR15","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1002\/jgt.3190070113","volume":"7","author":"DW Matula","year":"1983","unstructured":"Matula, D.W.: Ramsey theory for graph connectivity. J. Graph Theory 7, 95\u2013105 (1983)","journal-title":"J. Graph Theory"},{"key":"2052_CR16","unstructured":"Tian Y.Z., Xu L.Q., Lai H.-J., Meng J.X.: On the sizes of $$k$$-edge-maximal $$r$$-uniform hypergraphs. \n                    arXiv:1802.08843v3"},{"key":"2052_CR17","unstructured":"Xu L. Q., Lai H.-J., Tian Y. Z.: On the sizes of vertex-$$k$$-maximal graphs (submitted)"},{"key":"2052_CR18","first-page":"231","volume":"67","author":"R Yuster","year":"2003","unstructured":"Yuster, R.: A note on graphs without $$k$$-connected subgraphs. Ars Combin. 67, 231\u2013235 (2003)","journal-title":"Ars Combin."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-019-02052-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00373-019-02052-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-019-02052-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,5]],"date-time":"2020-06-05T23:28:06Z","timestamp":1591399686000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00373-019-02052-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,7]]},"references-count":18,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["2052"],"URL":"https:\/\/doi.org\/10.1007\/s00373-019-02052-z","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,7]]},"assertion":[{"value":"1 August 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 June 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}