{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T07:49:54Z","timestamp":1726213794102},"reference-count":15,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2016,10,6]],"date-time":"2016-10-06T00:00:00Z","timestamp":1475712000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004083","name":"Ministry of Science ICT and Future Planning","doi-asserted-by":"publisher","award":["NRF\u20102014R1A2A1A11050999"],"id":[{"id":"10.13039\/501100004083","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2017,6]]},"abstract":"Abstract<\/jats:title>A graph is intrinsically knotted if every embedding contains a nontrivially knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, K<\/jats:italic>7<\/jats:sub> and the 13 graphs obtained from K<\/jats:italic>7<\/jats:sub> by moves, are the only minor minimal intrinsically knotted graphs with 21 edges [1, 9, 11, 12]. This set includes exactly one bipartite graph, the Heawood graph. In this article we classify the intrinsically knotted bipartite graphs with at most 22 edges. Previously known examples of intrinsically knotted graphs of size 22 were those with KS graph minor and the 168 graphs in the K<\/jats:italic>3, 3, 1, 1<\/jats:sub> and families. Among these, the only bipartite example with no Heawood subgraph is Cousin 110 of the family. We show that, in fact, this is a complete listing. That is, there are exactly two graphs of size at most 22 that are minor minimal bipartite intrinsically knotted: the Heawood graph and Cousin 110.<\/jats:p>","DOI":"10.1002\/jgt.22091","type":"journal-article","created":{"date-parts":[[2016,10,13]],"date-time":"2016-10-13T00:45:05Z","timestamp":1476319505000},"page":"568-584","source":"Crossref","is-referenced-by-count":7,"title":["Bipartite Intrinsically Knotted Graphs with 22 Edges"],"prefix":"10.1002","volume":"85","author":[{"given":"Hyoungjun","family":"Kim","sequence":"first","affiliation":[{"name":"INSTITUTE OF MATHEMATICAL SCIENCES EWHA WOMANS UNIVERSITY SEOUL 03760 KOREA"}]},{"given":"Thomas","family":"Mattman","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS AND STATISTICS CALIFORNIA STATE UNIVERSITY CHICO CA 95929"}]},{"given":"Seungsang","family":"Oh","sequence":"additional","affiliation":[{"name":"DEPARTMENT OF MATHEMATICS KOREA UNIVERSITY SEOUL 02841 KOREA"}]}],"member":"311","published-online":{"date-parts":[[2016,10,6]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.2140\/involve.2016.9.591"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021821650700552X"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070410"},{"key":"e_1_2_7_5_1","first-page":"107","article-title":"The moves does not preserve intrinsic knottedness","volume":"45","author":"Flapan E.","year":"2008","journal-title":"Osaka J Math"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10017"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2014.14.1801"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2011.252.407"},{"key":"e_1_2_7_9_1","first-page":"47","article-title":"A sufficient condition for intrinsic knotting of bipartite graphs","volume":"27","author":"Huck S.","year":"2010","journal-title":"Kobe J Math"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216510008455"},{"key":"e_1_2_7_11_1","first-page":"435","article-title":"Some remarks on knots and links in spatial graphs","volume":"90","author":"Kohara T.","year":"1992","journal-title":"Knots (Osaka, 1990)"},{"key":"e_1_2_7_12_1","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2015.15.3305"},{"key":"e_1_2_7_13_1","doi-asserted-by":"publisher","DOI":"10.2140\/agt.2011.11.691"},{"key":"e_1_2_7_14_1","doi-asserted-by":"crossref","unstructured":"R.Motwani A.Raghunathan andH.Saran Constructive results from graph minors; linkless embeddings Proceedings of the 29th Annual Symposium on Foundations of Computer Science IEEE (1988) pp.398\u2013409.","DOI":"10.1109\/SFCS.1988.21956"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.5209\/rev_REMA.2007.v20.n2.16496"},{"key":"e_1_2_7_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.08.001"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22091","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22091","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22091","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T03:40:43Z","timestamp":1696563643000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22091"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,6]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["10.1002\/jgt.22091"],"URL":"https:\/\/doi.org\/10.1002\/jgt.22091","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,6]]}}}