{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:51:50Z","timestamp":1787323910638,"version":"build-2736575974"},"reference-count":15,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>We consider the problem of how much edge connectivity is necessary to force a graph $G$ to contain a fixed graph $H$ as an immersion. We show that if the maximum degree in $H$ is $\\Delta$, then all the examples of $\\Delta$-edge connected graphs which do not contain $H$ as a weak immersion must have a treelike decomposition called a tree-cut decomposition of bounded width. If we consider strong immersions, then it is easy to see that there are arbitrarily highly edge connected graphs which do not contain a fixed clique $K_t$ as a strong immersion. We give a structure theorem which roughly characterizes those highly edge connected graphs which do not contain $K_t$ as a strong immersion.<\/jats:p>","DOI":"10.1137\/130924056","type":"journal-article","created":{"date-parts":[[2014,3,25]],"date-time":"2014-03-25T11:39:49Z","timestamp":1395747589000},"page":"503-520","source":"Crossref","is-referenced-by-count":27,"title":["Immersions in Highly Edge Connected Graphs"],"prefix":"10.1137","volume":"28","author":[{"given":"D\u00e1niel","family":"Marx","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Wollan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,3,25]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.11.043"},{"key":"atypb2","unstructured":"M. Chudnovsky, Z. Dvorak, T. Klimosova, and P. Seymour,<i>Immersion in Four-Edge-Connected Graphs<\/i> manuscript, 2012."},{"key":"atypb4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.37236\/2533","volume":"20","author":"DeVos M.","year":"2013","journal-title":"Electron. J. Combin."},{"key":"atypb5","unstructured":"R. Diestel,<i>Graph Theory<\/i> 3rd ed. Springer-Verlag, Berlin, 2006."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.1013"},{"key":"atypb7","unstructured":"Z. Dvorak and T. Klimosova,<i>Strong Immersions and Maximum Degree<\/i> preprint, ariv:1304.0728 [math.CO], 2013."},{"key":"atypb8","first-page":"274","author":"Giannopolous A.","year":"2013","journal-title":"Berlin"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01917434"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/0404010"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(86)90023-4"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(90)90063-6"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(91)90061-N"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2009.07.003"},{"key":"atypb15","unstructured":"P. Wollan,<i>The Structure of Graphs not Admitting a Fixed Immersion<\/i> preprint, arXiv:1302.3867 [math.CO], 2013."},{"key":"atypb16","unstructured":"F. Zickfeld,<i>Geometric and Combinatorial Structures on Graphs<\/i> Ph.D. thesis, Technische Universit\u00e4t Berlin, Berlin, 2008."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130924056","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:15:39Z","timestamp":1787321739000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130924056"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1137\/130924056"],"URL":"https:\/\/doi.org\/10.1137\/130924056","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}