{"id":"https://openalex.org/W2167845365","doi":"https://doi.org/10.1155/s0161171204306216","title":"The chromatic sum of a graph: history and recent developments","display_name":"The chromatic sum of a graph: history and recent developments","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2167845365","doi":"https://doi.org/10.1155/s0161171204306216","mag":"2167845365"},"language":"en","primary_location":{"id":"doi:10.1155/s0161171204306216","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204306216","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/149326.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2004/149326.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085143853","display_name":"Ewa Kubicka","orcid":null},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ewa Kubicka","raw_affiliation_strings":["Department of Mathematics, University of Louisville"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Louisville","institution_ids":["https://openalex.org/I142740786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5085143853"],"corresponding_institution_ids":["https://openalex.org/I142740786"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3459,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.65076284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2004","issue":"30","first_page":"1563","last_page":"1573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9402999877929688,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7675853967666626},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6961497664451599},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6732386350631714},{"id":"https://openalex.org/keywords/windmill-graph","display_name":"Windmill graph","score":0.560984194278717},{"id":"https://openalex.org/keywords/friendship-graph","display_name":"Friendship graph","score":0.5503409504890442},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.535222053527832},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5252004265785217},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.518937349319458},{"id":"https://openalex.org/keywords/critical-graph","display_name":"Critical graph","score":0.49563443660736084},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.482757031917572},{"id":"https://openalex.org/keywords/foster-graph","display_name":"Foster graph","score":0.47875159978866577},{"id":"https://openalex.org/keywords/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.4555746912956238},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.434208482503891},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.18945151567459106},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14943835139274597}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7675853967666626},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6961497664451599},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6732386350631714},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.560984194278717},{"id":"https://openalex.org/C70488441","wikidata":"https://www.wikidata.org/wiki/Q5504427","display_name":"Friendship graph","level":5,"score":0.5503409504890442},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.535222053527832},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5252004265785217},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.518937349319458},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.49563443660736084},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.482757031917572},{"id":"https://openalex.org/C68996132","wikidata":"https://www.wikidata.org/wiki/Q3115485","display_name":"Foster graph","level":5,"score":0.47875159978866577},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.4555746912956238},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.434208482503891},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.18945151567459106},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14943835139274597}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/s0161171204306216","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204306216","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/149326.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:149326","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2004/149326.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:122710aac9134cd2b62d5f818deadeaa","is_oa":true,"landing_page_url":"https://doaj.org/article/122710aac9134cd2b62d5f818deadeaa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 30, Pp 1563-1573 (2004)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/S0161171204306216","is_oa":false,"landing_page_url":"https://doi.org/10.1155/S0161171204306216","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1155/s0161171204306216","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204306216","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/149326.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2167845365.pdf","grobid_xml":"https://content.openalex.org/works/W2167845365.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W194283047","https://openalex.org/W1556157567","https://openalex.org/W1885547793","https://openalex.org/W1980672031","https://openalex.org/W1987585312","https://openalex.org/W2000545501","https://openalex.org/W2019683022","https://openalex.org/W2037513717","https://openalex.org/W2068849088","https://openalex.org/W2078054726","https://openalex.org/W2082242399","https://openalex.org/W2083692180","https://openalex.org/W2084318417","https://openalex.org/W2089342001","https://openalex.org/W2140411614","https://openalex.org/W2141749671","https://openalex.org/W2952913262","https://openalex.org/W6602990649","https://openalex.org/W6606312767"],"related_works":["https://openalex.org/W2332295289","https://openalex.org/W2092041285","https://openalex.org/W4248987388","https://openalex.org/W2359595284","https://openalex.org/W2897657622","https://openalex.org/W2355004170","https://openalex.org/W2028417235","https://openalex.org/W1989256506","https://openalex.org/W2269219693","https://openalex.org/W1508428315"],"abstract_inverted_index":{"The":[0,19,78],"chromatic":[1,34,40,45,62],"sum":[2,9,41],"of":[3,10,21,28,39,52,65,87],"a":[4,22,66],"graph":[5,23],"is":[6,24,42,80],"the":[7,25,50],"smallest":[8],"colors":[11,29,53],"among":[12],"all":[13],"proper":[14],"colorings":[15],"with":[16,74],"natural":[17,37],"numbers.":[18,58],"strength":[20,64],"minimum":[26],"number":[27],"necessary":[30],"to":[31],"obtain":[32],"its":[33],"sum.":[35],"A":[36],"generalization":[38],"optimum":[43],"cost":[44],"partition":[46],"(OCCP)":[47],"problem,":[48],"where":[49],"costs":[51],"can":[54],"be":[55],"arbitrary":[56],"positive":[57],"Existing":[59],"results":[60],"about":[61],"sum,":[63],"graph,":[67],"and":[68,89],"OCCP":[69],"problem":[70],"are":[71],"presented":[72],"together":[73],"some":[75,85],"recent":[76],"developments.":[77],"focus":[79],"on":[81],"polynomial":[82],"algorithms":[83],"for":[84],"families":[86],"graphs":[88],"NP\u2010completeness":[90],"issues.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
