{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T23:41:36Z","timestamp":1649115696607},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p> An equitable (k, d)-coloring is a (k, d)-coloring that is also equitable. In this paper, we raise a conjecture that if G is a graph such that for each edge xy \u2208 E(G), the sum d(x) + d(y) at most 2r + 1, then G has a d-relaxed equitable coloring with r + 1 - d colors. We prove that if graph G meet d(x) + d(y) \u2264 2r for every edge xy \u2208 E(G) and |G| = rs, then [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830912500425","type":"journal-article","created":{"date-parts":[[2012,8,6]],"date-time":"2012-08-06T08:31:23Z","timestamp":1344241883000},"page":"1250042","source":"Crossref","is-referenced-by-count":0,"title":["A QUESTION ON RELAXED EQUITABLE COLORING"],"prefix":"10.1142","volume":"04","author":[{"given":"WEI","family":"GAO","sequence":"first","affiliation":[{"name":"Department of Mathematics, Soochow University, Jiangsu Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FEN","family":"ZHOU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Zhaotong Teachers' College, Yunnan Zhaotong 657000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,8,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190100207"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s003730050020"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2011.08.001"},{"key":"rf5","unstructured":"A.\u00a0Hajnal and E.\u00a0Szemer\u00e9di, Combinatorial Theory and Its Application, eds. P.\u00a0Erd\u00f6s, A.\u00a0R\u00e9nyi and V. T.\u00a0S\u00f3s (North-Holland, London, 1970)\u00a0pp. 601\u2013623."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2007.07.003"},{"key":"rf7","first-page":"55","volume":"1","author":"Kostochka A. V.","journal-title":"Oberwolfach Rep."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306007899"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140113"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500425","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:43:44Z","timestamp":1565131424000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500425"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,6]]},"references-count":9,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,8,6]]},"published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.1142\/S1793830912500425"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500425","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,6]]}}}