{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T00:36:16Z","timestamp":1787358976889,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["648527"],"award-info":[{"award-number":["648527"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010446","name":"Institute for Basic Science","doi-asserted-by":"publisher","award":["IBS-R029-C1"],"award-info":[{"award-number":["IBS-R029-C1"]}],"id":[{"id":"10.13039\/501100010446","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2018R1D1A1B07050294"],"award-info":[{"award-number":["NRF-2018R1D1A1B07050294"]}],"id":[{"id":"10.13039\/501100003725","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>A class $\\mathcal{F}$ of graphs has the induced Erd\u00f6s--P\u00f3sa property if there exists a function $f$ such that for every graph $G$ and every positive integer $k$, $G$ contains either $k$ pairwise vertex-disjoint induced subgraphs that belong to $\\mathcal{F}$, or a vertex set of size at most $f(k)$ hitting all induced copies of graphs in $\\mathcal{F}$. Kim and Kwon in [ J. Combin. Theory Ser. B, 145 (2020), pp. 65--112] showed that for a cycle $C_{\\ell}$ of length $\\ell$, the class of $C_{\\ell}$-subdivisions has the induced Erd\u00f6s--P\u00f3sa property if and only if $\\ell\\le 4$. In this paper, we investigate whether or not the class of $H$-subdivisions has the induced Erd\u00f6s--P\u00f3sa property for other graphs $H$. We completely settle the case when $H$ is a forest or a complete bipartite graph. Regarding the general case, we identify necessary conditions on $H$ for the class of $H$-subdivisions to have the induced Erd\u00f6s--P\u00f3sa property. For this, we provide three basic constructions that are useful for proving that the class of the subdivisions of a graph does not have the induced Erd\u00f6s--P\u00f3sa property. Among remaining graphs, we prove that if $H$ is the diamond, the 1-pan, or the 2-pan, then the class of $H$-subdivisions has the induced Erd\u00f6s--P\u00f3sa property.<\/jats:p>","DOI":"10.1137\/18m1226166","type":"journal-article","created":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T12:27:27Z","timestamp":1617798447000},"page":"597-636","source":"Crossref","is-referenced-by-count":1,"title":["Packing and Covering Induced Subdivisions"],"prefix":"10.1137","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1820-1962","authenticated-orcid":true,"given":"O-joung","family":"Kwon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4646-7602","authenticated-orcid":true,"given":"Jean-Florent","family":"Raymond","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,4,7]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1962-10847-7"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2004.03.059"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-007-0047-0"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2017.06.034"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/17M1148542"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-017-0313-5"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2018.08.009"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"R. Diestel,\n                      Graph Theory\n                      , 5th ed., Grad. Texts in Math. 173, Springer, Berlin, 2017,https:\/\/doi.org\/10.1007\/978-3-662-53622-3.","DOI":"10.1007\/978-3-662-53622-3_7"},{"key":"atypb9","first-page":"49","author":"Erd\u00f6s P.","year":"2009","journal-title":"MA"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.5486\/PMD.1962.9.1-2.02"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21776"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/140997889"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02066678"},{"key":"atypb14","first-page":"1399","author":"Jansen B. M. P.","year":"2017","journal-title":"Philadelphia"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2020.05.002"},{"key":"atypb16","unstructured":"C.H. Liu,\n                      Packing Topological Minors Half-Integrally\n                      , preprint,https:\/\/arxiv.org\/abs\/1707.07221, 2017."},{"key":"atypb17","unstructured":"B. Mohar and C. Thomassen,\n                      Graphs on Surfaces\n                      , Johns Hopkins University Press, Baltimore, MD, 2001."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1994.1054"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2017.01.004"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2016.12.025"},{"key":"atypb21","first-page":"87","author":"Reed B. 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