{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T16:20:23Z","timestamp":1725466823317},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2013,10,16]],"date-time":"2013-10-16T00:00:00Z","timestamp":1381881600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2014,9]]},"abstract":"Abstract<\/jats:title>In 1989, Lescure and Meyniel proved, for , that every d<\/jats:italic>\u2010chromatic graph contains an immersion of , and in 2003 Abu\u2010Khzam and Langston conjectured that this holds for all d<\/jats:italic>. In 2010, DeVos, Kawarabayashi, Mohar, and Okamura proved this conjecture for . In each proof, the d<\/jats:italic>\u2010chromatic assumption was not fully utilized, as the proofs only use the fact that a d<\/jats:italic>\u2010critical graph has minimum degree at least . DeVos, Dvo\u0159\u00e1k, Fox, McDonald, Mohar, and Scheide show the stronger conjecture that a graph with minimum degree has an immersion of fails for and with a finite number of examples for each value of d<\/jats:italic>, and small chromatic number relative to d<\/jats:italic>, but it is shown that a minimum degree of 200d<\/jats:italic> does guarantee an immersion of .In this paper, we show that the stronger conjecture is false for and give infinite families of examples with minimum degree and chromatic number , , or that do not contain an immersion of . Our examples can be up to \u2010edge\u2010connected. We show that two of Haj\u00f3s' operations preserve immersions of . We conclude with some open questions, and the conjecture that a 2\u2010edge\u2010connected graph G<\/jats:italic> with minimum degree and more than vertices of degree at least has an immersion of .<\/jats:p>","DOI":"10.1002\/jgt.21770","type":"journal-article","created":{"date-parts":[[2013,10,16]],"date-time":"2013-10-16T06:17:37Z","timestamp":1381904257000},"page":"1-18","source":"Crossref","is-referenced-by-count":7,"title":["Constructing Graphs with No Immersion of Large Complete Graphs"],"prefix":"10.1002","volume":"77","author":[{"given":"Karen L.","family":"Collins","sequence":"first","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE WESLEYAN UNIVERSITY MIDDLETOWN CT 06459"}]},{"given":"Megan E.","family":"Heenehan","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE EASTERN CONNECTICUT STATE UNIVERSITY WILLIMANTIC CT 06226"}]}],"member":"311","published-online":{"date-parts":[[2013,10,16]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20308"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45071-8_40"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90049-3"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.05.001"},{"key":"e_1_2_7_6_1","unstructured":"M.DeVos Z.Dvo\u0159\u00e1k J.Fox J.McDonald B.Mohar andD.Scheide Minimum degree condition forcing complete graph immersion submitted (2011)."},{"key":"e_1_2_7_7_1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.26493\/1855-3974.112.b74","article-title":"Immersing small complete graphs","volume":"3","author":"DeVos M.","year":"2010","journal-title":"Ars Math Contemp"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2012.02.002"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-27.1.85"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20283"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2011.09.066"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00080-7"},{"key":"e_1_2_7_13_1","first-page":"133","article-title":"\u00dcber eine Klassifikation der Strekenkomplexe","volume":"88","author":"Hadwiger H.","year":"1943","journal-title":"Vierteljahrsschr. 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