{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T10:44:47Z","timestamp":1649155487917},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> A k-fold n-coloring of a graph G is an assignment of k distinct colors to each vertex of G from n colors, such that adjacent vertices receive no colors in common. If G has a k-fold n-coloring, then say G is k-fold n-colorable. Denote the kth chromatic number of G by \u03c7<jats:sub>k<\/jats:sub>(G), i.e. \u03c7<jats:sub>k<\/jats:sub>(G) = min {n : G is k- fold n- colorable }. We show that every planar graph with odd girth at least 6k + 1(k = 3) or 6k - 1(k = 2) can be k-fold (2k + 1)-colorable. <\/jats:p>","DOI":"10.1142\/s1793830911001164","type":"journal-article","created":{"date-parts":[[2011,7,13]],"date-time":"2011-07-13T13:20:39Z","timestamp":1310563239000},"page":"171-184","source":"Crossref","is-referenced-by-count":0,"title":["k-FOLD (2k + 1)-COLORING OF PLANAR GRAPHS"],"prefix":"10.1142","volume":"03","author":[{"given":"YUEHUA","family":"BU","sequence":"first","affiliation":[{"name":"College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Zhejiang, Jinhua 321004, P. R. China"}]},{"given":"YUDIE","family":"WU","sequence":"additional","affiliation":[{"name":"College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Zhejiang, Jinhua 321004, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(200002)33:2<109::AID-JGT5>3.0.CO;2-F"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s003730200007"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.07.015"},{"key":"rf5","first-page":"2791","volume":"33","author":"Ren G.","journal-title":"Sci. China Ser. A: Math."},{"key":"rf6","series-title":"Wiley-Interscience Series in Discrete Mathematics and Optimization","volume-title":"Fractional Graph Theory","author":"Scheinerman E. R.","year":"1997"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(76)90010-1"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911001164","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:13:04Z","timestamp":1565194384000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911001164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6]]},"references-count":6,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,6]]}},"alternative-id":["10.1142\/S1793830911001164"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911001164","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6]]}}}