{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T12:51:34Z","timestamp":1698238294861},"reference-count":7,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5331,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A <jats:italic>rooted graph<\/jats:italic> is a pair (<jats:italic>G, x<\/jats:italic>) where <jats:italic>G<\/jats:italic> is a simple undirected graph and <jats:italic>x<\/jats:italic> \u03f5 <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>). If <jats:italic>G<\/jats:italic> if rooted at <jats:italic>x<\/jats:italic>, then its <jats:italic>rotation number h(G, x)<\/jats:italic> is teh minimum number of edges in a graph <jats:italic>F<\/jats:italic>, of the same order as <jats:italic>G<\/jats:italic>, such that for all <jats:italic>v<\/jats:italic> \u03f5 <jats:italic>V(F)<\/jats:italic> we can find a copy of <jats:italic>G<\/jats:italic> in <jats:italic>F<\/jats:italic> with the root <jats:italic>x<\/jats:italic> at <jats:italic>v<\/jats:italic>. Rotation numbers for complete bipartite graphs were itroduced in [4] by Cockayne and Lorimer. Several cases were evaluated by Bollob\u00e1s and Cockayne in [2], and in this paper we give a full solution.<\/jats:p>","DOI":"10.1002\/jgt.3190160107","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:51:54Z","timestamp":1181285514000},"page":"61-71","source":"Crossref","is-referenced-by-count":1,"title":["Rotation numers for complete bipartite graphs"],"prefix":"10.1002","volume":"16","author":[{"given":"Julie","family":"Haviland","sequence":"first","affiliation":[]},{"given":"Andrew","family":"Thomason","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Extrmal Graph Theory","author":"Bollob\u00e1s B.","year":"1978"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190060404"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190080108"},{"key":"e_1_2_1_5_2","unstructured":"E. J.CockayneandP. J.Lorimer On rotation numbers for complete bipartite graphs. University of Victoria Department of Mathematics Report DM\u2010186\u2010IR (1979)."},{"key":"e_1_2_1_6_2","first-page":"203","article-title":"Rotation numbers for unions of triangles and circuits","volume":"17","author":"Cockayne E. J.","year":"1983","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_7_2","unstructured":"J.Haviland Cliques and independent sets. Ph.D.thesis University of Cambridge (1989)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788140"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190160107","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190160107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T14:21:29Z","timestamp":1698070889000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190160107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,3]]}},"alternative-id":["10.1002\/jgt.3190160107"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190160107","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}