{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:51:49Z","timestamp":1767340309704},"reference-count":0,"publisher":"Wiley","issue":"30","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>The <jats:italic>chromatic sum<\/jats:italic> of a graph is the\nsmallest sum of colors among all proper colorings with natural\nnumbers. The <jats:italic>strength<\/jats:italic> of a graph is the minimum number\nof colors necessary to obtain its chromatic sum. A natural\ngeneralization of chromatic sum is <jats:italic>optimum cost chromatic\npartition (OCCP)<\/jats:italic> problem, where the costs of colors can be\narbitrary positive numbers. Existing results about chromatic sum,\nstrength of a graph, and OCCP problem are presented together with\nsome recent developments. The focus is on polynomial algorithms\nfor some families of graphs and NP\u2010completeness issues.<\/jats:p>","DOI":"10.1155\/s0161171204306216","type":"journal-article","created":{"date-parts":[[2004,7,20]],"date-time":"2004-07-20T11:34:48Z","timestamp":1090323288000},"page":"1563-1573","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["The chromatic sum of a graph: history and recent developments"],"prefix":"10.1155","volume":"2004","author":[{"given":"Ewa","family":"Kubicka","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,7,18]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/149326.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/149326.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204306216","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T20:05:21Z","timestamp":1723061121000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204306216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"30","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204306216"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204306216","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-06-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-07-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}