{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T14:40:10Z","timestamp":1716475210037},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>A k-partition V<jats:sub>1<\/jats:sub>, V<jats:sub>2<\/jats:sub>, \u2026, V<jats:sub>k<\/jats:sub>of a graph G is said to be balanced if -1 \u2264 |V<jats:sub>i<\/jats:sub>| - |V<jats:sub>j<\/jats:sub>| \u2264 1 for 1 \u2264 i, j \u2264 k. The maximum balanced k-partition problem asks for a balanced k-partition V<jats:sub>1<\/jats:sub>, V<jats:sub>2<\/jats:sub>, \u2026, V<jats:sub>k<\/jats:sub>of a graph that maximizes e(V<jats:sub>1<\/jats:sub>, V<jats:sub>2<\/jats:sub>, \u2026, V<jats:sub>k<\/jats:sub>) which is the total number of edges with ends in distinct ones of V<jats:sub>1<\/jats:sub>, V<jats:sub>2<\/jats:sub>, \u2026, V<jats:sub>k<\/jats:sub>. Let G be a graph with m edges, and let r be the maximum number of vertex-disjoint 2-paths, where a 2-path stands for a path of length 2. We show that G admits a balanced 3-partition V<jats:sub>1<\/jats:sub>, V<jats:sub>2<\/jats:sub>, V<jats:sub>3<\/jats:sub>such that [Formula: see text]. We also present, for each real number 3 \u2264 p &lt; 6, a sufficient condition that G admits a maximum balanced 3-partition V<jats:sub>1<\/jats:sub>, V<jats:sub>2<\/jats:sub>, V<jats:sub>3<\/jats:sub>with [Formula: see text], where e(V<jats:sub>i<\/jats:sub>) denotes the number of edges of G with both ends in V<jats:sub>i<\/jats:sub>.<\/jats:p>","DOI":"10.1142\/s1793830914500207","type":"journal-article","created":{"date-parts":[[2014,1,23]],"date-time":"2014-01-23T09:54:02Z","timestamp":1390470842000},"page":"1450020","source":"Crossref","is-referenced-by-count":0,"title":["MAXIMUM BALANCED 3-PARTITIONS OF GRAPHS"],"prefix":"10.1142","volume":"06","author":[{"given":"HAIYAN","family":"LI","sequence":"first","affiliation":[{"name":"Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, P. R. China"}]},{"given":"BAOGANG","family":"XU","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,3,19]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01876314"},{"key":"rf2","first-page":"473","volume":"19","author":"Bollob\u00e1s B.","journal-title":"Combinatorica"},{"key":"rf3","first-page":"185","volume":"10","author":"Bollob\u00e1s B.","journal-title":"Bolyai Soc. Math. Stud."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10062"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10174"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.11.030"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(76)90059-1"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2013.06.002"},{"key":"rf12","first-page":"651","volume":"56","author":"Li H.","journal-title":"Acta Math. Sinica. (Chin. Ser.)"},{"key":"rf13","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1002\/jgt.20421","volume":"63","author":"Xu B.","journal-title":"J. Graph Theory"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.03.029"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2008.08.007"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548311000204"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500207","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T14:23:43Z","timestamp":1716474223000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,19]]},"references-count":14,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,3,19]]},"published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.1142\/S1793830914500207"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500207","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,19]]}}}