{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T16:58:52Z","timestamp":1648918732049},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p> A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Hadwiger conjectures that every k-chromatic graph contains K<jats:sub>k<\/jats:sub> as a minor. It implies that every graph G on n vertices has a [Formula: see text] as a minor, where \u03b1(G) is the independence number of G. In this paper, we consider the graphs G with independence number two. It is proved that G has a K<jats:sub>l<\/jats:sub>-minor using prevertices of size one or two, where [Formula: see text] and \u03ba is the connectivity of G. It is also proved that G has a [Formula: see text]-minor if [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830909000026","type":"journal-article","created":{"date-parts":[[2009,4,8]],"date-time":"2009-04-08T04:55:25Z","timestamp":1239166525000},"page":"121-125","source":"Crossref","is-referenced-by-count":0,"title":["THE CLIQUE MINOR OF GRAPHS WITH INDEPENDENCE NUMBER TWO"],"prefix":"10.1142","volume":"01","author":[{"given":"SHIYOU","family":"PANG","sequence":"first","affiliation":[{"name":"School of Science, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, P. R. China"}]},{"given":"LIANYING","family":"MIAO","sequence":"additional","affiliation":[{"name":"School of Science, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, P. R. China"}]},{"given":"QINGBO","family":"SUN","sequence":"additional","affiliation":[{"name":"School of Science, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, P. R. China"}]},{"given":"ZHENGKE","family":"MIAO","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Xuzhou Normal University, Xuzhou, Jiangsu, 221116, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2007.04.003"},{"key":"rf2","first-page":"85","volume":"27","author":"Dirac G. A.","journal-title":"J. London Math. Soc."},{"key":"rf3","series-title":"Graduate Texts in Mathematics","volume-title":"Graph Theory","volume":"173","author":"Diestel R.","year":"1997"},{"key":"rf4","first-page":"71","volume":"13","author":"Duchet P.","journal-title":"Ann. Discrete Math."},{"key":"rf5","first-page":"133","volume":"88","author":"Hadwiger H.","journal-title":"Ges. Z\u00fcrich"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20268"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01202354"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01594196"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830909000026","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:17:29Z","timestamp":1565129849000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830909000026"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3]]},"references-count":8,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2009,3]]}},"alternative-id":["10.1142\/S1793830909000026"],"URL":"https:\/\/doi.org\/10.1142\/s1793830909000026","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3]]}}}