{"id":"https://openalex.org/W2141749671","doi":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<354::aid-jgt4>3.0.co;2-b","title":"Coloring of trees with minimum sum of colors","display_name":"Coloring of trees with minimum sum of colors","publication_year":1999,"publication_date":"1999-12-01","ids":{"openalex":"https://openalex.org/W2141749671","doi":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<354::aid-jgt4>3.0.co;2-b","mag":"2141749671"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199912)32:4<354::aid-jgt4>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<354::aid-jgt4>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101911266","display_name":"Tao Jiang","orcid":"https://orcid.org/0000-0003-3833-4498"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tao Jiang","raw_affiliation_strings":["University of Illinois, Urbana, IL 61801-2975","University of Illinois, Urbana, IL 61801\u20102975"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL 61801-2975","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois, Urbana, IL 61801\u20102975","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101911266","display_name":"Tao Jiang","orcid":"https://orcid.org/0000-0003-3833-4498"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tao Jiang","raw_affiliation_strings":["University of Illinois, Urbana, IL 61801-2975","University of Illinois, Urbana, IL 61801\u20102975"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL 61801-2975","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois, Urbana, IL 61801\u20102975","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017595199","display_name":"Douglas B. West","orcid":"https://orcid.org/0000-0001-8818-1667"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Douglas B. West","raw_affiliation_strings":["University of Illinois, Urbana, IL 61801-2975"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL 61801-2975","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017595199","https://openalex.org/A5101911266"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.2359009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"4","first_page":"354","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.8167999982833862,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.8167999982833862,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8769551515579224},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8167508840560913},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.588329553604126},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5574126839637756},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5273203253746033},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.4425395727157593},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.43996870517730713},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.430841326713562},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.42753303050994873},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.42589670419692993},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.17266282439231873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05883803963661194},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.05388370156288147}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8769551515579224},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8167508840560913},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.588329553604126},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5574126839637756},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5273203253746033},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.4425395727157593},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.43996870517730713},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.430841326713562},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.42753303050994873},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.42589670419692993},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.17266282439231873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05883803963661194},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.05388370156288147},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199912)32:4<354::aid-jgt4>3.0.co;2-b","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199912)32:4<354::aid-jgt4>3.0.co;2-b","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.6094","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.6094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/9904140v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.33.9227","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.9227","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~j-tao/tree.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.54","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.54","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~west/treesum.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1975068100","https://openalex.org/W1980672031","https://openalex.org/W2083692180","https://openalex.org/W2089342001"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W3169197204","https://openalex.org/W4291316360","https://openalex.org/W2585997002","https://openalex.org/W2380525562","https://openalex.org/W398688634","https://openalex.org/W4229747356","https://openalex.org/W4297911588","https://openalex.org/W149461665","https://openalex.org/W2046652778"],"abstract_inverted_index":{"The":[0,19,53],"chromatic":[1,31],"sum":[2,9],"of":[3,10,25],"a":[4,40],"graph":[5],"is":[6,21,55],"the":[7,22,30],"smallest":[8],"colors":[11,26],"among":[12],"all":[13],"proper":[14],"colorings":[15],"with":[16,42],"natural":[17],"numbers.":[18],"strength":[20,43],"minimum":[23],"number":[24],"needed":[27],"to":[28],"achieve":[29],"sum.":[32],"We":[33],"construct":[34],"for":[35],"each":[36],"positive":[37],"integer":[38],"k":[39,44],"tree":[41],"that":[45],"has":[46],"maximum":[47],"degree":[48],"only":[49],"2k":[50],"\u2212":[51],"2.":[52],"result":[54],"best":[56],"possible.":[57],"\u00a9":[58],"1999":[59,70],"John":[60],"Wiley":[61],"&":[62],"Sons,":[63],"Inc.":[64],"J":[65],"Graph":[66],"Theory":[67],"32:":[68],"354\u2013358,":[69]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}