{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:55:50Z","timestamp":1787324150467,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["321904558"],"award-info":[{"award-number":["321904558"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We prove that every graph $G$ contains either $k$ edge-disjoint $K_4$-subdivisions or a set $X$ of at most $\\ensuremath{O}(k^8 \\log k)$ edges such that $G-X$ does not contain any $K_4$-subdivision. This shows that $K_4$-subdivisions have the edge-Erd\u00f6s--P\u00f3sa property.<\/jats:p>","DOI":"10.1137\/18m1216511","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T10:23:12Z","timestamp":1615803792000},"page":"392-430","source":"Crossref","is-referenced-by-count":2,"title":["$K_4$-Subdivisions Have the Edge-Erd\u00f6s--P\u00f3sa Property"],"prefix":"10.1137","volume":"35","author":[{"given":"Henning","family":"Bruhn-Fujimoto","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthias","family":"Heinlein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,3,15]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1153169"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"H. Bruhn, M. Heinlein, and F. Joos,\n                      The edge-Erd\u00f6s-P\u00f3sa property\n                      , in preparation, 2018.","DOI":"10.1007\/s00493-017-3669-x"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/17M1148542"},{"key":"atypb5","unstructured":"H. Bruhn, F. Joos, and O. Schaudt,\n                      Erd\u00f6s-P\u00f3sa Property for Labelled Minors: 2-Connected Minors\n                      , ArXiv e-prints, 2018."},{"key":"atypb6","first-page":"195","volume":"52","author":"Dejter I. J.","year":"1987","journal-title":"Colloq. Math. Soc. J\u00e1nos Bolyai"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"R. Diestel,\n                      Graph Theory\n                      , 4th ed., Springer, Heidelberg, 2010.","DOI":"10.1007\/978-3-642-14279-6"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(92)90041-D"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1965-035-8"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"S. Fiorini, G. Joret, and D. R. Wood,\n                      Excluded Forest Minors and the Erd\u00f6s-P\u00f3sa Property\n                      , ArXiv e-prints, 2012.","DOI":"10.1017\/S0963548313000266"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02066678"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/100786423"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.03.004"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"W. Mader,\n                      \u00dcber die Maximalzahl kantendisjunkter A-Wege\n                      , Arch. Math. (Basel), 30 (1978), pp. 325-336.","DOI":"10.1007\/BF01226062"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2012.05.004"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2016.03.004"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90030-4"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120111"},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"W. Cames van Batenburg, T. Huynh, G. Joret, and J.F. Raymond,\n                      A Tight Erd\u00f6s-P\u00f3sa Function for Planar Minors\n                      , arXiv:187.04969, 2018.","DOI":"10.19086\/aic.10807"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-011-2551-5"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1216511","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:19:28Z","timestamp":1787321968000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1216511"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/18M1216511"],"URL":"https:\/\/doi.org\/10.1137\/18m1216511","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}