{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T18:15:41Z","timestamp":1693332941694},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T00:00:00Z","timestamp":1562630400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T00:00:00Z","timestamp":1562630400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2019,11]]},"DOI":"10.1007\/s00493-019-3856-z","type":"journal-article","created":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T14:19:44Z","timestamp":1562681984000},"page":"1081-1104","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Extremal Function for Bipartite Linklessly Embeddable Graphs"],"prefix":"10.1007","volume":"39","author":[{"given":"Rose","family":"McCarty","sequence":"first","affiliation":[]},{"given":"Robin","family":"Thomas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,7,9]]},"reference":[{"key":"3856_CR1","first-page":"101","volume":"123","author":"R Bacher","year":"1995","unstructured":"R. Bacher and Y. Colin de Verdi\u00e8re: Multiplicit\u00e9s des valeurs propres et transformations \u00e9toile-triangle des graphes, Bulletin de la Soci\u00e9t\u00e9Math\u00e9matique de France123 (1995), 101\u2013117.","journal-title":"Bulletin de la Soci\u00e9t\u00e9Math\u00e9matique de France"},{"key":"3856_CR2","first-page":"195","volume-title":"Europ. J. Combin.","author":"B Bollob\u00e1s","year":"1980","unstructured":"B. Bollob\u00e1s, P. A. Catlin and P. Erd\u0151s: Hadwiger\u2019s conjecture is true for almost every graph, Europ. J. Combin. 1 (1980), 195\u2013199."},{"key":"3856_CR3","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/0095-8956(90)90093-F","volume":"50","author":"Y de Colin Verdi\u00e8re","year":"1990","unstructured":"Y. Colin de Verdi\u00e8re: Sur un nouvel invariant des graphes et un crit\u00e8re de pla- narit\u00e9, J. Combin. Theory Ser. B50 (1990), 11\u201321.","journal-title":"J. Combin. Theory Ser. B"},{"key":"3856_CR4","first-page":"109","volume":"46","author":"W de la Fernandez Vega","year":"1983","unstructured":"W. Fernandez de la Vega: On the maximum density of graphs which have no subtractions to K\ns, Discrete Math. 46 (1983), 109\u2013110.","journal-title":"On the maximum density of graphs which have no subtractions to Ks, Discrete Math."},{"key":"3856_CR5","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.jctb.2018.02.001","volume":"131","author":"K Hendrey","year":"2018","unstructured":"K. Hendrey and D. R. Wood: The extremal function for Petersen minors, J. Combin. Theory Ser. B131 (2018), 220\u2013253.","journal-title":"J. Combin. Theory Ser. B"},{"key":"3856_CR6","doi-asserted-by":"publisher","first-page":"5515","DOI":"10.1090\/tran\/6512","volume":"368","author":"G Kalai","year":"2016","unstructured":"G. Kalai, E. Nevo and I. Novik: Bipartite rigidity, Trans. Amer. Math. Soc.368 (2016), 5515\u20135545.","journal-title":"Trans. Amer. Math. Soc."},{"key":"3856_CR7","unstructured":"A. V. Kostochka: The minimum Hadwiger number for graphs with a given mean degree of vertices, Metody Diskret. Analiz.38 (1982), 37\u201358 (in Russian)."},{"key":"3856_CR8","unstructured":"A. V. Kostochka: A lower bound for the product of the Hadwiger numbers of a graph and its complement, Combinatorial analysis 8 (1989), 50\u201362 (in Russian)."},{"key":"3856_CR9","doi-asserted-by":"publisher","first-page":"4435","DOI":"10.1016\/j.disc.2007.08.041","volume":"308","author":"A V Kostochka","year":"2008","unstructured":"A. V. Kostochka and N. Prince: On K\ns,t minors in graphs with given average degree, Discrete Math.308 (2008), 4435\u20134445.","journal-title":"Discrete Math."},{"key":"3856_CR10","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.ejc.2004.02.002","volume":"26","author":"D K\u00fchn","year":"2005","unstructured":"D. K\u00fchn and D. Osthus: Forcing unbalanced complete bipartite minors, Europ. J. Combin.26 (2005), 75\u201381.","journal-title":"Europ. J. Combin."},{"key":"3856_CR11","doi-asserted-by":"publisher","first-page":"1275","DOI":"10.1090\/S0002-9939-98-04244-0","volume":"126","author":"L Lov\u00e1sz","year":"1998","unstructured":"L. Lov\u00e1sz and A. Schrijver: A Borsuk theorem for antipodal links and a spectral characterization of linklessly embeddable graphs, Proc. Amer. Math. Soc.126 (1998), 1275\u20131285.","journal-title":"Proc. Amer. Math. Soc."},{"key":"3856_CR12","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1007\/BF01350657","volume":"178","author":"W Mader","year":"1968","unstructured":"W. Mader: Homomorphies\u00e4tze f\u00fcr Graphen, Math. Ann.178 (1968), 154\u2013168.","journal-title":"Math. Ann."},{"key":"3856_CR13","volume-title":"The Extremal Function and Colin de Verdi\u00e8re Graph Parameter","author":"R McCarty","year":"1706","unstructured":"R. McCarty: The Extremal Function and Colin de Verdi\u00e8re Graph Parameter, arXiv:1706.07451."},{"key":"3856_CR14","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/s00493-007-2168-x","volume":"27","author":"E Nevo","year":"2007","unstructured":"E. Nevo: Embeddability and stresses of graphs, Combinatorica27 (2007), 465\u2013472.","journal-title":"Combinatorica"},{"key":"3856_CR15","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1006\/jctb.1995.1032","volume":"64","author":"N Robertson","year":"1995","unstructured":"N. Robertson, P. D. Seymour and R. Thomas: Sachs\u2019 linkless embedding conjecture, J. Combin. Theory Ser. B64 (1995), 185\u2013227.","journal-title":"J. Combin. Theory Ser. B"},{"key":"3856_CR16","unstructured":"H. Sachs: On a spatial analogue of Kuratowski\u2019s theorem on planar graphs - an open problem, Proceedings of a Conference held in Lagow, Poland, February 10\u201313, 1981, Lecture Notes in Mathematics, Vol. 1018, Springer-Verlag, Berlin, 1983."},{"key":"3856_CR17","first-page":"649","volume-title":"Finite and infinite sets","author":"H Sachs","year":"1984","unstructured":"H. Sachs: On spatial representation of finite graphs, Colloquia Mathematica So-cietatis J\u00e1nos Bolyai, 37. Finite and infinite sets, (eds. A. Hajnal, L. Lov\u00e1sz and V. T. Sos), North-Holland, Budapest 1984, 649\u2013662."},{"key":"3856_CR18","volume-title":"The Colin de Verdi\u00e8re parameter, excluded minors, and the spectral radius","author":"M Tait","year":"1703","unstructured":"M. Tait: The Colin de Verdi\u00e8re parameter, excluded minors, and the spectral radius, arXiv:1703.09732."},{"key":"3856_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejc.2018.07.010","volume":"75","author":"R Thomas","year":"2019","unstructured":"R. Thomas and Y. Yoo: The extremal functions for triangle-free graphs with excluded minors, Europ. J. Combin.75 (2019), 1\u201310.","journal-title":"Europ. J. Combin."},{"key":"3856_CR20","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1017\/S0305004100061521","volume":"95","author":"A Thomason","year":"1984","unstructured":"A. Thomason: An extremal function for contractions of graphs, Math. Proc. Cambridge Philos. Soc.95 (1984), 261\u2013265.","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"3856_CR21","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1006\/jctb.2000.2013","volume":"81","author":"A Thomason","year":"2001","unstructured":"A. Thomason: The extremal function for complete minors, J. Combin. Theory Ser. B81 (2001), 318\u2013338.","journal-title":"J. Combin. Theory Ser. B"},{"key":"3856_CR22","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1007\/BF01594196","volume":"114","author":"K Wagner","year":"1937","unstructured":"K. Wagner: Uber eine Eigenschaft der ebenen Komplexe, Math. Ann.114 (1937), 570\u2013590.","journal-title":"Math. Ann."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-019-3856-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-019-3856-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-019-3856-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,7]],"date-time":"2020-07-07T23:36:50Z","timestamp":1594165010000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-019-3856-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,9]]},"references-count":22,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,11]]}},"alternative-id":["3856"],"URL":"https:\/\/doi.org\/10.1007\/s00493-019-3856-z","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,9]]},"assertion":[{"value":"29 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 July 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}